CS_441_2023_Spring_January_31,_2023.vtt

WEBVTT Kind: captions; Language: en-US

NOTE
Created on 2024-02-07T20:53:13.8059397Z by ClassTranscribe

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It seems like there's like.

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Yes, it's OK.

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Alright, good morning everybody.

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So I thought it I was trying to figure

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out why this seems like there's a lot

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of light on the screen, but I can't

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figure it out.

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I thought it was interesting that this

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for this picture.

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And.

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So I'm generating all of these with

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Dolly.

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This one was a dirt Rd.

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splits around a large gnarly tree

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fractal art.

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But I thought it was really funny how

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it without my bidding it put like some

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kind of superhero or something behind

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the tree there's like some looks like

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there's like some superhero that's like

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flying in and.

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I don't know where that came from.

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Can you guys see the screen OK?

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Seems a little faded.

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But.

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OK I.

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Yeah, I put the lights are on all off.

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But those are still on.

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Alright, let me just take one second.

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All right.

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Anyway, I'll move with it.

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Alright, so.

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And so for some Logistics, I wanted to

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I never got to introduce some of the

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TAS because the couple couldn't be here

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in the first day and I kept forgetting.

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So, Josh, are you here?

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OK, cool if you want to just actually.

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I can give my mic.

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If you want to just introduce yourself

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a little bit, you can say like what

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kind of.

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Yeah.

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Hi, everyone.

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I'm Josh.

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I've been applying machine learning to

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autonomous cars and airplanes.

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Cool.

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Thank you.

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And cassette, cassette.

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Yeah.

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OK hey everyone, I'm a TA for CS441 and

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I have experience with NLP majorly.

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Thank you.

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Great.

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Thank you.

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And I don't think Peter's here, but

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Peter, are you here, OK.

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Usually has a conflict on Tuesday, so

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also we have Pedro is a.

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A pro stock course Assistant.

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So it's not like a regular TA, but

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he's.

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Doing a postdoc with Nancy Amato.

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And here is helping out with the online

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course for a couple semesters.

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And so he's helping out with this

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course and he's.

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One of the things he's doing is holding

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office hours, and so especially if you

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have, if you want help with your

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projects or homeworks, they're like

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higher level advice, then he can be a

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really good resource for that.

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So I know a lot of people want to meet

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with me about their side projects,

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which is also fine, you're welcome to

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do that.

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But he's also a good person for that.

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Alright, so just as a reminder for

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anybody who wasn't here, the first

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lecture, all the notes and everything

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are on this web page.

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So make sure that you go there and sign

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up for CampusWire where announcements

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will be made.

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Also, I sent a survey by e-mail and I

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got a little bit of responses last

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night.

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Do you take some time to respond to it

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please?

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There's two parts.

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One is just asking for feedback about

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like piece of the course.

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And stuff like that.

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And.

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One part is asking about your interests

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for some of the possible.

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Challenges that I'll pick for final

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project and so basically for the final

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project there will be 3 challenges that

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are like pre selected.

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But if you don't want to do those, you

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can also just do some benchmark that's

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online or you can even do a custom

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task.

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And I'll post the specifications for

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final project soon as homework 2.

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Also, just based on the feedback I've

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seen so far, I think nobody thinks it's

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way too easy or too slow.

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Some people think it's much too fast

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and too hard.

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So I'm going to take some time on

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Thursday to Reconsolidate and present.

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Kind of go over what we've done so far,

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talk in more depth or maybe not more

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depth, but at least go over the

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concepts.

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And the algorithms and a little bit of

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code now that you've had a first pass

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edit.

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So I'll tap the brakes a little bit to

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do that because I think it's really

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important that these that everyone is

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really solid on these fundamentals.

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And I know that there's a pretty big

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range of backgrounds of people taking

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the course, many people from other

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departments.

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As well as other different kinds of.

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Of like academic foundations.

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Alright.

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So just to recap what we talked about

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in the last few lectures, very briefly,

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we talked about Nearest neighbor.

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And the superpower is the nearest

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neighbor are that it can instantly

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learn new classes.

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You can just add a new example to your

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training set.

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And since there's no model that has to

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be like tuned, you can just learn super

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quickly.

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And it's also a pretty good predictor

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from either one or many examples.

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So it's a really good.

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It's a really good algorithm to have in

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your tool belt as a baseline and

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sometimes as a best performer.

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We also talked about Naive bees.

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Night Bayes is not a great performer as

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like a full algorithm, but it's often

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a.

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It's an important concept because it's

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often part of an assumption that you

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make when you're trying to model

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probabilities that you'll assume that

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the different features are independent

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given the thing that you're trying to

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predict.

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It does have its pros, so the pros are

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that it's really fast to estimate even

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if you've got a lot of data.

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And if you don't have a lot of data and

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you're trying to get a probabilistic

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classifier, then it might be your best

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choice.

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Because of its strong assumptions, you

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can get decent estimates on those

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single variable functions from even

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limited data.

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We talked about logistic regression.

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Logistic regression is another super

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widely used classifier.

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I think the AML book says that SVM is

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should be or like go to as a first as

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like a first thing you try, but in my

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opinion Logistic Regression is.

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It's very effective.

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It's a very effective predictor if you

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have high dimensional features and it

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also provides good confidence

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estimates, meaning that.

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You get not only most likely class, but

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the probability that prediction is

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correct and those probabilities fairly

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trustworthy.

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We also talked about Linear Regression,

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where you're fitting a line to a set of

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points.

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And you can extrapolate to predict like

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new values that are outside of your

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Training range.

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And so.

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Linear regression is also useful for

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explaining relationships you're very

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commonly see, like trend lines.

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That's just Linear Regression.

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And you can predict continuous values

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from many variables in linear

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regression is also like probably the

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most common tool for.

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For things like, I don't know, like

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economics or analyzing.

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Yeah, time series analyzing like fMRI

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data or all kinds of scientific and

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economic analysis.

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So almost all algorithms involve these

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Nearest neighbor, logistic regression

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or linear regression.

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And the reason that there's thousand

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papers published in the last 10 years

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or so, probably a lot more than that

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actually, is that.

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Is really the feature learning, so it's

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getting the right representation so

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that when you feed that representation

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into these like Linear models or

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Nearest neighbor, you get good results.

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And so.

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Pretty much the rest of what we're

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going to learn in the supervised

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learning section of the course is how

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to learn features.

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So I did want to just briefly go over

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the homework and remind you that it's

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due on February 6th on Monday.

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And I'll be going over some related

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things again in more detail on

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Thursday.

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But there's two parts to the main

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homework.

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There's Digit Classification where

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you're trying to predict a label zero

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to 9 based on a 28 by 28 image.

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These images get reshaped into like a

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single vector, so you have a feature

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vector that corresponds to the pixel

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intensities of the image.

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And then you have to do K and Naive

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Bayes, linear logistic regression.

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And plot the Error versus.

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A plot Error versus Training size to

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get a sense for like how performance

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changes as you vary the number of

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training examples.

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And then to select the best parameter

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using validation set which is a really

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hyper parameter.

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Tuning is like something that you do

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all the time in machine learning.

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The second problem is Temperature

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Regression.

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So I got this Temperature.

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This data set of like the temperature

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is a big cities in the US and then

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made-up a problem from it.

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So the problem is to try to predict the

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next day's temperature in Cleveland

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which stays zero given all the previous

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temperatures.

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And these features have meanings.

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Every feature is some previous is, like

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the temperature of 1 in the big cities

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from one in the past five days.

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But you can kind of.

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You don't really need to know those

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meanings in order to solve the problem

00:12:48.110 --> 00:12:48.480
again.

00:12:48.480 --> 00:12:50.780
You essentially just have a feature

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vector of a bunch of continuous values

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in this case, and you're trying to

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predict a new continuous value, which

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is Cleveland Cleveland's temperature in

00:13:00.460 --> 00:13:01.240
the next day.

00:13:02.010 --> 00:13:04.545
And again you can use KNN and a Bayes

00:13:04.545 --> 00:13:06.000
and now Linear Regression.

00:13:07.020 --> 00:13:08.935
KNN implementation will be essentially

00:13:08.935 --> 00:13:11.440
the same for these A2 line change of

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code because now instead of predicting

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a categorical variable, you're

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predicting a continuous variable.

00:13:18.440 --> 00:13:20.580
So if K is greater than one, you

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average the predictions for Regression

00:13:23.770 --> 00:13:26.280
where for the Classification you choose

00:13:26.280 --> 00:13:27.430
the most common prediction.

00:13:28.580 --> 00:13:29.840
That's the only change.

00:13:29.840 --> 00:13:31.590
Naive Bayes does change quite a bit

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because you're using a different

00:13:32.710 --> 00:13:33.590
probabilistic model.

00:13:34.360 --> 00:13:36.710
And remember that there's one lecture

00:13:36.710 --> 00:13:38.670
slide that has the derivation for how

00:13:38.670 --> 00:13:40.545
you do the inference for nibbies under

00:13:40.545 --> 00:13:41.050
the setting.

00:13:42.330 --> 00:13:44.760
And then for linear and logistic

00:13:44.760 --> 00:13:46.820
regression you're able to use the

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modules in sklearn.

00:13:49.890 --> 00:13:51.680
And then the final part is to identify

00:13:51.680 --> 00:13:53.550
the most important features using L1

00:13:53.550 --> 00:13:54.320
Linear Regression.

00:13:55.030 --> 00:13:57.160
So the reason that we use.

00:13:58.020 --> 00:13:59.810
And when we do like.

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Linear and logistic regression, we're

00:14:03.170 --> 00:14:03.580
trying.

00:14:03.580 --> 00:14:05.228
We're mainly trying to fit the data.

00:14:05.228 --> 00:14:06.600
We're trying to come up with a model

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that fits the data or fits our

00:14:08.340 --> 00:14:09.920
predictions given the features.

00:14:10.630 --> 00:14:13.720
But also we often express some

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preference.

00:14:15.190 --> 00:14:19.892
Over the model, in particular that the

00:14:19.892 --> 00:14:21.669
weights don't get too large, and the

00:14:21.670 --> 00:14:25.170
reason for that is to avoid like

00:14:25.170 --> 00:14:27.070
overfitting or over relying on

00:14:27.070 --> 00:14:30.410
particular features, as well as to

00:14:30.410 --> 00:14:34.795
improve the generalization to new data

00:14:34.795 --> 00:14:36.209
and generalization.

00:14:36.210 --> 00:14:37.810
Research shows that if you can fit

00:14:37.810 --> 00:14:39.220
something with smaller weights, then

00:14:39.220 --> 00:14:42.013
you're more likely to generalize to new

00:14:42.013 --> 00:14:42.209
data.

00:14:44.640 --> 00:14:46.550
And here we're going to use it for

00:14:46.550 --> 00:14:47.520
feature selection, yeah?

00:14:58.910 --> 00:15:02.370
The so the parameters are.

00:15:02.370 --> 00:15:04.510
You're talking about 1/3.

00:15:04.510 --> 00:15:07.825
OK, so for Naive Bayes the parameter is

00:15:07.825 --> 00:15:10.430
the prior, so that's like the alpha of

00:15:10.430 --> 00:15:11.010
like your.

00:15:11.670 --> 00:15:14.903
In the, it's the initial count, so you

00:15:14.903 --> 00:15:15.882
have a Naive Bayes.

00:15:15.882 --> 00:15:17.360
You have a prior that's essentially

00:15:17.360 --> 00:15:19.200
that you pretend like you've seen all

00:15:19.200 --> 00:15:20.230
combinations of.

00:15:20.950 --> 00:15:23.930
Of things that you're counting, you

00:15:23.930 --> 00:15:26.210
pretend that you see alpha times, and

00:15:26.210 --> 00:15:28.510
so that kind of gives you a bias

00:15:28.510 --> 00:15:30.200
towards estimating that everything's

00:15:30.200 --> 00:15:33.170
equally likely, and that alpha is a

00:15:33.170 --> 00:15:34.190
parameter that you can use.

00:15:34.810 --> 00:15:36.270
You can learn using validation.

00:15:37.010 --> 00:15:39.920
For Logistic Regression, it's the

00:15:39.920 --> 00:15:42.650
Lambda which is your weight on the

00:15:42.650 --> 00:15:43.760
regularization term.

00:15:45.650 --> 00:15:48.180
And for K&N, it's your K, which is the

00:15:48.180 --> 00:15:49.320
number of nearest neighbors you

00:15:49.320 --> 00:15:49.710
consider.

00:15:57.960 --> 00:15:58.220
Yeah.

00:16:00.180 --> 00:16:03.284
So the K&N is.

00:16:03.284 --> 00:16:05.686
It's almost the same whether you're

00:16:05.686 --> 00:16:08.260
doing Regression or Classification.

00:16:08.260 --> 00:16:09.980
When you find the K nearest neighbors,

00:16:09.980 --> 00:16:11.790
it's the exact same code.

00:16:11.790 --> 00:16:14.016
The difference is that if you're doing

00:16:14.016 --> 00:16:15.270
Regression, you're trying to predict

00:16:15.270 --> 00:16:16.200
continuous values.

00:16:16.200 --> 00:16:19.340
So if K is greater than one, then you

00:16:19.340 --> 00:16:21.532
want to average those continuous values

00:16:21.532 --> 00:16:23.150
to get your final prediction.

00:16:23.850 --> 00:16:26.060
And if you're doing Classification, you

00:16:26.060 --> 00:16:28.490
find the most common label instead of

00:16:28.490 --> 00:16:29.803
averaging because you don't want to

00:16:29.803 --> 00:16:31.470
say, well it could be a four, it could

00:16:31.470 --> 00:16:31.980
be a 9.

00:16:31.980 --> 00:16:33.110
So I'm going to like split the

00:16:33.110 --> 00:16:34.270
difference and say it's a 6.

00:16:42.030 --> 00:16:45.420
That are averaging just that you so

00:16:45.420 --> 00:16:47.600
like if K&N returns like the

00:16:47.600 --> 00:16:54.870
temperatures of 1012 and 13 then you

00:16:54.870 --> 00:16:57.190
would say that the average temperature

00:16:57.190 --> 00:16:59.530
is like 11.3 or whatever that works out

00:16:59.530 --> 00:16:59.730
to.

00:17:04.600 --> 00:17:06.440
Yeah, at the end, if K is greater than

00:17:06.440 --> 00:17:09.333
one, then you take the arithmetic mean

00:17:09.333 --> 00:17:11.210
of the average of the.

00:17:11.940 --> 00:17:14.560
Predictions of your K nearest

00:17:14.560 --> 00:17:14.970
neighbors.

00:17:16.590 --> 00:17:16.790
Yeah.

00:17:18.610 --> 00:17:20.560
And so you could also get a variance

00:17:20.560 --> 00:17:22.370
from that, which you don't need to do

00:17:22.370 --> 00:17:24.500
for the homework, but so as a result

00:17:24.500 --> 00:17:26.550
you can have some like confidence bound

00:17:26.550 --> 00:17:27.840
on your estimate as well.

00:17:30.050 --> 00:17:31.780
Alright then you have stretch goals,

00:17:31.780 --> 00:17:32.170
so.

00:17:32.850 --> 00:17:34.100
Stretch goals are.

00:17:35.130 --> 00:17:37.000
Mainly intended for people taking the

00:17:37.000 --> 00:17:39.020
four credit version, but you can anyone

00:17:39.020 --> 00:17:39.510
can try them.

00:17:40.240 --> 00:17:42.570
So there's just improving the MNIST

00:17:42.570 --> 00:17:44.370
classification, like some ideas.

00:17:44.370 --> 00:17:47.360
Or you could try to crop around the

00:17:47.360 --> 00:17:49.000
Digit, or you could make sure that

00:17:49.000 --> 00:17:51.840
they're all centered, or do some

00:17:51.840 --> 00:17:53.410
whitening or other kinds of feature

00:17:53.410 --> 00:17:54.340
transformations.

00:17:55.430 --> 00:17:56.770
Improving Temperature Regression.

00:17:56.770 --> 00:18:00.070
To be honest, I'm not sure exactly how

00:18:00.070 --> 00:18:01.829
much this can be improved or how to

00:18:01.830 --> 00:18:02.280
improve it.

00:18:03.030 --> 00:18:04.720
Again, there's.

00:18:04.720 --> 00:18:07.370
What I would do is try like subtracting

00:18:07.370 --> 00:18:08.110
off the mean.

00:18:08.110 --> 00:18:09.220
For example, you can.

00:18:10.380 --> 00:18:12.370
You can normalize your features before

00:18:12.370 --> 00:18:15.540
you do the fitting by subtracting off

00:18:15.540 --> 00:18:16.750
means and dividing by steering

00:18:16.750 --> 00:18:17.410
deviations.

00:18:17.410 --> 00:18:18.140
That's one idea.

00:18:19.060 --> 00:18:22.320
But we'll look at it after submissions

00:18:22.320 --> 00:18:24.095
if it turns out that.

00:18:24.095 --> 00:18:27.020
So the targets I Choose are because I

00:18:27.020 --> 00:18:29.273
was able to do like some simple things

00:18:29.273 --> 00:18:32.383
to bring down the Error by a few tenths

00:18:32.383 --> 00:18:33.510
of a percent.

00:18:33.510 --> 00:18:35.000
So I kind of figured that if you do

00:18:35.000 --> 00:18:36.346
more things, you'll be able to bring it

00:18:36.346 --> 00:18:38.420
down further, but it's hard to tell so.

00:18:39.240 --> 00:18:40.960
If you do this and you put a lot of

00:18:40.960 --> 00:18:42.600
effort into it, describe your effort

00:18:42.600 --> 00:18:45.594
and we'll assign points even if you

00:18:45.594 --> 00:18:47.680
even if it turns out that there's not

00:18:47.680 --> 00:18:48.640
like a big improvement.

00:18:48.640 --> 00:18:50.676
So don't stress out if you can't get

00:18:50.676 --> 00:18:51.609
like 119.

00:18:52.450 --> 00:18:54.200
RMS a year or something like that.

00:18:55.130 --> 00:18:55.335
Right.

00:18:55.335 --> 00:18:57.306
The last one is to generate a train

00:18:57.306 --> 00:18:58.806
set, train Test, Classification set.

00:18:58.806 --> 00:19:00.380
So this actually means don't like

00:19:00.380 --> 00:19:02.020
generate it out of MNIST to create

00:19:02.020 --> 00:19:02.804
synthetic data.

00:19:02.804 --> 00:19:05.020
So you can Naive Bayes make certain

00:19:05.020 --> 00:19:05.405
assumptions.

00:19:05.405 --> 00:19:07.180
So if you generate your data according

00:19:07.180 --> 00:19:09.390
to those Assumptions, you should be

00:19:09.390 --> 00:19:11.900
able to create a problem that we're

00:19:11.900 --> 00:19:13.520
Naive bees can outperform the other

00:19:13.520 --> 00:19:13.980
methods.

00:19:18.970 --> 00:19:22.130
So for these homeworks, make sure that

00:19:22.130 --> 00:19:24.020
you of course read the assignment.

00:19:24.020 --> 00:19:25.040
Read the tips.

00:19:25.530 --> 00:19:26.210


00:19:27.060 --> 00:19:29.190
And then you should be adding code to

00:19:29.190 --> 00:19:30.045
the starter code.

00:19:30.045 --> 00:19:31.610
The starter code doesn't really solve

00:19:31.610 --> 00:19:33.030
the problems for you, but it loads the

00:19:33.030 --> 00:19:34.570
data and gives you some examples.

00:19:34.570 --> 00:19:38.160
So for example, for example, there's a.

00:19:38.810 --> 00:19:41.340
In the Regression, I think it includes

00:19:41.340 --> 00:19:43.710
like a baseline where it computes RMSE

00:19:43.710 --> 00:19:46.450
and median absolute error, so that

00:19:46.450 --> 00:19:48.760
function can essentially be reused

00:19:48.760 --> 00:19:50.060
later to compute the errors.

00:19:51.120 --> 00:19:53.073
And that baseline gives you some idea

00:19:53.073 --> 00:19:55.390
of like what kind of performance you

00:19:55.390 --> 00:19:55.870
might get.

00:19:55.870 --> 00:19:57.320
Like you should beat that baseline

00:19:57.320 --> 00:19:58.620
because that's just based on a single

00:19:58.620 --> 00:19:58.940
feature.

00:20:00.300 --> 00:20:02.980
And then you complete the report and

00:20:02.980 --> 00:20:04.940
make sure to include expected points.

00:20:04.940 --> 00:20:07.040
So when the grader is graded they will

00:20:07.040 --> 00:20:09.140
essentially just say if they disagree

00:20:09.140 --> 00:20:09.846
with you.

00:20:09.846 --> 00:20:12.470
So you if you claim like 10 points but

00:20:12.470 --> 00:20:14.345
something was wrong then they might say

00:20:14.345 --> 00:20:16.310
you lose like 3 points for this reason

00:20:16.310 --> 00:20:20.340
and so that streamlines their grading.

00:20:21.930 --> 00:20:23.580
The assignment, the report Submit your

00:20:23.580 --> 00:20:26.070
notebook and either if you just have

00:20:26.070 --> 00:20:28.800
one file, submitting the IPYNB is fine

00:20:28.800 --> 00:20:29.890
or otherwise you can zip it.

00:20:30.860 --> 00:20:32.220
And that's it.

00:20:33.960 --> 00:20:34.620
Yeah, question.

00:20:41.730 --> 00:20:47.160
So you need in three Credit was at 450,

00:20:47.160 --> 00:20:47.640
is that right?

00:20:48.650 --> 00:20:50.810
So think I think in the three credit

00:20:50.810 --> 00:20:52.300
you need 450 points.

00:20:53.660 --> 00:20:55.430
Each assignment without doing any

00:20:55.430 --> 00:20:56.230
stretch goals.

00:20:56.230 --> 00:20:58.620
Each assignment is worth 100 points and

00:20:58.620 --> 00:21:01.240
the final project is worth 50 points.

00:21:01.240 --> 00:21:02.673
I mean sorry, the final projects worth

00:21:02.673 --> 00:21:03.460
100 points also.

00:21:04.150 --> 00:21:06.310
So if you're in the three Credit

00:21:06.310 --> 00:21:08.210
version and you don't do any stretch

00:21:08.210 --> 00:21:10.960
goals, and you do all the assignments

00:21:10.960 --> 00:21:12.500
and you do the final project, you will

00:21:12.500 --> 00:21:13.570
have more points than you need.

00:21:14.190 --> 00:21:17.740
So the so you can kind of pick

00:21:17.740 --> 00:21:19.270
something that you don't want to do and

00:21:19.270 --> 00:21:20.910
skip it if you're in the three credit

00:21:20.910 --> 00:21:24.100
course and or like if you just are

00:21:24.100 --> 00:21:26.330
already a machine learning guru, you

00:21:26.330 --> 00:21:29.290
can do like 3 assignments with all the

00:21:29.290 --> 00:21:31.630
extra parts and then take a vacation.

00:21:32.920 --> 00:21:34.720
If you're in the four credit version,

00:21:34.720 --> 00:21:37.490
then you will have to do some of the.

00:21:37.670 --> 00:21:39.520
Some of the stretch goals in order to

00:21:39.520 --> 00:21:41.470
get your full points, which are 550.

00:21:49.580 --> 00:21:52.715
Alright, so now I'm going to move on to

00:21:52.715 --> 00:21:54.180
the main topic.

00:21:54.180 --> 00:21:57.340
So we've seen so far, we've seen 2 main

00:21:57.340 --> 00:21:59.116
choices for how to use the features.

00:21:59.116 --> 00:22:01.025
We could do Nearest neighbor when we

00:22:01.025 --> 00:22:03.200
use all the features jointly in order

00:22:03.200 --> 00:22:05.280
to find similar examples, and then we

00:22:05.280 --> 00:22:06.970
predict the most similar label.

00:22:07.910 --> 00:22:10.160
Or we can use a linear model where

00:22:10.160 --> 00:22:11.980
essentially you're making a prediction

00:22:11.980 --> 00:22:14.530
out of a of all the feature values.

00:22:16.070 --> 00:22:18.490
But there's some other things that are

00:22:18.490 --> 00:22:20.270
kind of intuitive, so.

00:22:21.220 --> 00:22:24.010
For example, if you consider this where

00:22:24.010 --> 00:22:26.260
you're trying to split the red X's from

00:22:26.260 --> 00:22:27.710
the Green O's.

00:22:28.370 --> 00:22:30.820
What's like another way that you might

00:22:30.820 --> 00:22:33.180
try to define what that Decision

00:22:33.180 --> 00:22:35.130
boundary is if you wanted to, say, tell

00:22:35.130 --> 00:22:35.730
somebody else?

00:22:35.730 --> 00:22:37.110
Like how do you identify whether

00:22:37.110 --> 00:22:38.770
something is a no?

00:22:52.240 --> 00:22:55.600
Yeah, I mean you so your jaw some kind

00:22:55.600 --> 00:22:56.200
of boundary.

00:22:57.150 --> 00:22:57.690
And.

00:22:58.620 --> 00:23:00.315
And one way that you might think about

00:23:00.315 --> 00:23:03.440
that is creating a kind of like simple

00:23:03.440 --> 00:23:04.220
rule like this.

00:23:04.220 --> 00:23:05.890
Like you might say that if.

00:23:06.600 --> 00:23:09.040
You basically draw a boundary, but if

00:23:09.040 --> 00:23:11.252
you want to specify you might say if X2

00:23:11.252 --> 00:23:15.820
is less than .6 and X2 is greater than

00:23:15.820 --> 00:23:16.500
two.

00:23:17.460 --> 00:23:21.480
And tX2, oops, that's just say X1 and

00:23:21.480 --> 00:23:22.082
the last one.

00:23:22.082 --> 00:23:24.630
And if X1 is less than seven then it's

00:23:24.630 --> 00:23:26.672
an O and otherwise it's an X.

00:23:26.672 --> 00:23:28.110
So basically you could create like a

00:23:28.110 --> 00:23:29.502
set of rules like that, right?

00:23:29.502 --> 00:23:32.161
So say if it meets these criteria then

00:23:32.161 --> 00:23:34.819
it's one class and if it meets these

00:23:34.820 --> 00:23:37.070
other criteria it's another class.

00:23:40.160 --> 00:23:42.930
And So what we're going to learn today

00:23:42.930 --> 00:23:45.280
is how we can try to learn these rules

00:23:45.280 --> 00:23:48.220
automatically, even if we have a lot of

00:23:48.220 --> 00:23:50.520
features in more complicated kinds of

00:23:50.520 --> 00:23:51.250
predictions.

00:23:52.920 --> 00:23:55.108
So this is basically the idea of

00:23:55.108 --> 00:23:55.744
Decision trees.

00:23:55.744 --> 00:23:58.490
So we all use Decision trees in our own

00:23:58.490 --> 00:24:00.264
life, even if we don't think about it

00:24:00.264 --> 00:24:00.812
that way.

00:24:00.812 --> 00:24:02.710
Like you often say, if this happens,

00:24:02.710 --> 00:24:04.121
I'll do that, and if it doesn't, then

00:24:04.121 --> 00:24:05.029
I'll do this other thing.

00:24:05.030 --> 00:24:06.685
That's like a Decision tree, right?

00:24:06.685 --> 00:24:10.400
You had some kind of criteria, and

00:24:10.400 --> 00:24:12.306
depending on the outcome of that

00:24:12.306 --> 00:24:13.886
criteria, you do one thing.

00:24:13.886 --> 00:24:16.680
And if it's the other way, if you get

00:24:16.680 --> 00:24:17.900
the other outcome, then you would be

00:24:17.900 --> 00:24:18.920
doing the other thing.

00:24:18.920 --> 00:24:20.310
And maybe you have a whole chain of

00:24:20.310 --> 00:24:22.090
them if I.

00:24:22.250 --> 00:24:23.700
If I have time today, I'm going to go

00:24:23.700 --> 00:24:25.990
to the grocery store, but if the car is

00:24:25.990 --> 00:24:27.330
not there then I'm going to do this

00:24:27.330 --> 00:24:28.480
instead and so on.

00:24:29.850 --> 00:24:32.370
All right, so in Decision trees, the

00:24:32.370 --> 00:24:34.500
Training is essentially to iteratively

00:24:34.500 --> 00:24:37.340
Choose the attribute and split in a

00:24:37.340 --> 00:24:40.080
split value that will best separate

00:24:40.080 --> 00:24:41.530
your classes from each other.

00:24:42.920 --> 00:24:44.610
Or if you're doing continuous values

00:24:44.610 --> 00:24:47.010
that kind of group things into similar

00:24:47.010 --> 00:24:48.240
prediction values.

00:24:49.480 --> 00:24:52.440
So for example you might say if these

00:24:52.440 --> 00:24:56.600
red circles are oranges and these

00:24:56.600 --> 00:24:59.264
triangles are lemons, where there

00:24:59.264 --> 00:25:01.090
oranges and lemons are plotted

00:25:01.090 --> 00:25:02.250
according to their width and their

00:25:02.250 --> 00:25:02.750
height.

00:25:02.750 --> 00:25:07.726
You might decide well if it's less than

00:25:07.726 --> 00:25:10.170
6.5 centimeters then.

00:25:10.170 --> 00:25:12.690
Or I'll use greater since it's there if

00:25:12.690 --> 00:25:14.190
it's greater than 6.5 centimeters.

00:25:15.450 --> 00:25:17.267
Then I'm going to split it into this

00:25:17.267 --> 00:25:19.410
section where it's like mostly oranges

00:25:19.410 --> 00:25:22.110
and if it's less than 6.5 centimeters

00:25:22.110 --> 00:25:24.395
width, then I'll split it into this

00:25:24.395 --> 00:25:26.220
section where it's mostly lemons.

00:25:27.250 --> 00:25:30.560
Neither of these a perfect split still.

00:25:30.560 --> 00:25:32.910
So then I go further and say if it was

00:25:32.910 --> 00:25:35.309
on this side of the split, if it's

00:25:35.310 --> 00:25:37.915
greater than 95 centimeter height then

00:25:37.915 --> 00:25:40.350
it's a lemon, and if it's less than

00:25:40.350 --> 00:25:42.130
that then it's a.

00:25:42.820 --> 00:25:43.760
Then it's an orange.

00:25:44.900 --> 00:25:46.660
And now that's like a pretty confident

00:25:46.660 --> 00:25:47.170
prediction.

00:25:47.930 --> 00:25:49.610
And then if I'm on this side then I can

00:25:49.610 --> 00:25:51.560
split it by height and say if it's less

00:25:51.560 --> 00:25:51.990
than.

00:25:53.690 --> 00:25:55.530
If it's greater than 6 centimeters then

00:25:55.530 --> 00:25:57.714
it's a lemon, and if it's less than 6

00:25:57.714 --> 00:25:59.450
centimeters then it's an orange.

00:25:59.450 --> 00:26:01.130
So you can like iteratively Choose a

00:26:01.130 --> 00:26:03.180
test and then keep splitting the data.

00:26:03.780 --> 00:26:06.510
And every time you choose a test, test

00:26:06.510 --> 00:26:09.510
another test that splits the data

00:26:09.510 --> 00:26:10.910
further according to what you're trying

00:26:10.910 --> 00:26:11.320
to predict.

00:26:12.270 --> 00:26:14.890
Essentially, this method Combines a

00:26:14.890 --> 00:26:16.760
feature selection and modeling with

00:26:16.760 --> 00:26:17.410
prediction.

00:26:18.670 --> 00:26:20.420
So at the end of this, you transform

00:26:20.420 --> 00:26:22.940
what we're two continuous values into

00:26:22.940 --> 00:26:24.770
these four discrete values.

00:26:25.450 --> 00:26:27.360
Of different chunks, different

00:26:27.360 --> 00:26:30.130
partitions of the feature space and for

00:26:30.130 --> 00:26:31.350
each of those.

00:26:32.420 --> 00:26:34.850
Each of those parts of the partition.

00:26:35.810 --> 00:26:38.360
You make a prediction.

00:26:39.240 --> 00:26:41.620
A partitioning is just when you take a

00:26:41.620 --> 00:26:44.390
continuous space and divide it up into

00:26:44.390 --> 00:26:46.850
different cells that cover the entire

00:26:46.850 --> 00:26:47.400
space.

00:26:47.400 --> 00:26:49.859
That's a partition where the cells

00:26:49.860 --> 00:26:51.040
don't overlap with each other.

00:26:54.340 --> 00:26:56.460
And then if you want to classify, once

00:26:56.460 --> 00:26:57.940
you've trained your tree, you get some

00:26:57.940 --> 00:26:59.450
new test sample and you want to know is

00:26:59.450 --> 00:27:01.450
that a lemon or an orange kind of looks

00:27:01.450 --> 00:27:01.920
in between.

00:27:02.610 --> 00:27:05.295
So you is it greater than 6.5

00:27:05.295 --> 00:27:05.740
centimeters?

00:27:05.740 --> 00:27:06.185
No.

00:27:06.185 --> 00:27:08.355
Is a tight greater than 6 centimeters?

00:27:08.355 --> 00:27:08.690
No.

00:27:08.690 --> 00:27:10.110
And so therefore it's an orange

00:27:10.110 --> 00:27:10.970
according to your rule.

00:27:13.260 --> 00:27:15.053
And you could take this tree and could

00:27:15.053 --> 00:27:17.456
you could rewrite it as a set of rules,

00:27:17.456 --> 00:27:20.560
like one rule is greater than 6.5,

00:27:20.560 --> 00:27:23.478
height greater than 9.5, another rule

00:27:23.478 --> 00:27:26.020
is greater than 65, height less than

00:27:26.020 --> 00:27:27.330
9.5, and so on.

00:27:27.330 --> 00:27:28.640
There's like 4 different rules

00:27:28.640 --> 00:27:31.180
represented by this tree, and each rule

00:27:31.180 --> 00:27:33.950
corresponds to some section of the

00:27:33.950 --> 00:27:36.440
feature space, and each rule yields

00:27:36.440 --> 00:27:37.140
some prediction.

00:27:40.950 --> 00:27:44.020
So here's another example with some

00:27:44.020 --> 00:27:45.580
discrete inputs.

00:27:45.580 --> 00:27:48.030
So here the prediction problem is to

00:27:48.030 --> 00:27:49.955
tell whether or not somebody's going to

00:27:49.955 --> 00:27:50.350
wait.

00:27:50.350 --> 00:27:52.440
If they go to a restaurant and they're

00:27:52.440 --> 00:27:54.173
told they have to wait, so do they wait

00:27:54.173 --> 00:27:55.160
or do they leave?

00:27:56.290 --> 00:27:58.170
And the features are things like

00:27:58.170 --> 00:28:00.160
whether there's an alternative nearby,

00:28:00.160 --> 00:28:02.240
whether there's a bar they can wait at,

00:28:02.240 --> 00:28:03.900
whether it's Friday or Saturday,

00:28:03.900 --> 00:28:05.289
whether they're Hungry, whether the

00:28:05.290 --> 00:28:07.106
restaurants full, what the price is,

00:28:07.106 --> 00:28:08.740
whether it's raining, whether they had

00:28:08.740 --> 00:28:10.560
a Reservation, what type of restaurant

00:28:10.560 --> 00:28:12.900
is, and they would wait time.

00:28:12.900 --> 00:28:14.747
And these are all categorical, so the

00:28:14.747 --> 00:28:16.100
wait time is split into different

00:28:16.100 --> 00:28:16.540
chunks.

00:28:20.660 --> 00:28:22.670
And so you could.

00:28:24.110 --> 00:28:27.810
You could train a tree from these

00:28:27.810 --> 00:28:29.820
categorical variables, and of course I

00:28:29.820 --> 00:28:31.590
will tell you more about like how you

00:28:31.590 --> 00:28:32.390
would learn this tree.

00:28:33.960 --> 00:28:35.670
But you might have a tree like this

00:28:35.670 --> 00:28:36.500
where you say.

00:28:37.730 --> 00:28:39.770
First, are there are there people in

00:28:39.770 --> 00:28:40.370
the restaurant?

00:28:40.370 --> 00:28:41.800
Patrons means like it's a restaurant

00:28:41.800 --> 00:28:42.684
full or not.

00:28:42.684 --> 00:28:46.310
If it's not full, then you leave right

00:28:46.310 --> 00:28:47.790
away because they're just being rude.

00:28:47.790 --> 00:28:49.330
If they tell, you have to wait I guess.

00:28:49.930 --> 00:28:52.140
If it's partly full then you'll wait,

00:28:52.140 --> 00:28:54.080
and if it's full then you then you have

00:28:54.080 --> 00:28:55.680
like consider further things.

00:28:55.680 --> 00:28:58.360
If it's a WaitEstimate, really short,

00:28:58.360 --> 00:28:58.990
then you wait.

00:28:58.990 --> 00:28:59.660
Is it really long?

00:28:59.660 --> 00:29:00.170
Then you don't.

00:29:00.960 --> 00:29:03.290
Otherwise, are you hungry?

00:29:03.290 --> 00:29:04.693
If you're not, then you'll wait.

00:29:04.693 --> 00:29:06.600
If you are, then you keep thinking.

00:29:06.600 --> 00:29:08.320
So you have like, all this series of

00:29:08.320 --> 00:29:08.820
choices.

00:29:10.350 --> 00:29:12.790
That these trees and practice like if

00:29:12.790 --> 00:29:14.230
you were to use a Decision tree on

00:29:14.230 --> 00:29:14.680
MNIST.

00:29:15.810 --> 00:29:17.600
Where the features are pretty weak

00:29:17.600 --> 00:29:19.510
individually, they're just like pixel

00:29:19.510 --> 00:29:20.140
values.

00:29:20.140 --> 00:29:21.610
You can imagine that this tree could

00:29:21.610 --> 00:29:23.160
get really complicated and long.

00:29:27.970 --> 00:29:28.390
Right.

00:29:28.390 --> 00:29:31.840
So just to mostly be state.

00:29:32.450 --> 00:29:34.080
And then Decision tree.

00:29:34.080 --> 00:29:36.410
The internal nodes are Test Attributes,

00:29:36.410 --> 00:29:38.150
so it's some kind of like feature.

00:29:38.150 --> 00:29:40.050
Attribute and feature are synonymous,

00:29:40.050 --> 00:29:41.110
they're the same thing.

00:29:41.830 --> 00:29:45.880
Some kind of feature attribute and.

00:29:45.960 --> 00:29:47.420
And if it's a continuous attribute then

00:29:47.420 --> 00:29:48.420
you have to have some kind of

00:29:48.420 --> 00:29:53.420
threshold, so width greater than 6.5 or

00:29:53.420 --> 00:29:54.650
is it raining or not?

00:29:54.650 --> 00:29:56.050
Those are two examples of.

00:29:56.740 --> 00:29:57.440
Of tests.

00:29:58.370 --> 00:29:59.984
Then depending on the outcome of that

00:29:59.984 --> 00:30:02.310
test, you split in different ways, and

00:30:02.310 --> 00:30:03.860
when you're Training, you split all

00:30:03.860 --> 00:30:05.935
your data according to that test, and

00:30:05.935 --> 00:30:07.960
then you're going to solve again within

00:30:07.960 --> 00:30:09.390
each of those nodes separately.

00:30:10.480 --> 00:30:11.570
For the next Test.

00:30:12.260 --> 00:30:14.110
Until you get to a leaf node, and at

00:30:14.110 --> 00:30:16.125
the leaf node you provide an output or

00:30:16.125 --> 00:30:18.532
a prediction, which could be, which in

00:30:18.532 --> 00:30:20.480
this case is a class, in this

00:30:20.480 --> 00:30:21.780
particular example whether it's a

00:30:21.780 --> 00:30:22.540
Linear orange.

00:30:25.060 --> 00:30:25.260
Yep.

00:30:29.360 --> 00:30:31.850
So the question is how does it Decision

00:30:31.850 --> 00:30:34.700
tree account for anomalies as in late

00:30:34.700 --> 00:30:36.480
mislabeled data or really weird

00:30:36.480 --> 00:30:37.260
examples or?

00:30:50.100 --> 00:30:52.370
So the so the question is like how does

00:30:52.370 --> 00:30:54.400
it Decision tree deal with weird or

00:30:54.400 --> 00:30:55.860
unlikely examples?

00:30:55.860 --> 00:30:58.020
And that's a good question because one

00:30:58.020 --> 00:31:00.200
of the things about a Decision tree is

00:31:00.200 --> 00:31:01.510
that if you train it.

00:31:02.350 --> 00:31:04.460
If you train it, if you train the full

00:31:04.460 --> 00:31:06.560
tree, then you can always.

00:31:06.560 --> 00:31:09.970
As long as the feature vectors for each

00:31:09.970 --> 00:31:11.560
sample are unique, you can always get

00:31:11.560 --> 00:31:13.470
perfect Classification Error.

00:31:13.470 --> 00:31:14.900
A tree has no bias.

00:31:14.900 --> 00:31:16.580
You can always like fit your training

00:31:16.580 --> 00:31:18.980
data perfectly because you just keep on

00:31:18.980 --> 00:31:20.530
chopping it into smaller and smaller

00:31:20.530 --> 00:31:22.070
bits until finally the answer.

00:31:22.800 --> 00:31:24.960
So as a result, that can be dangerous

00:31:24.960 --> 00:31:26.767
because if you do have some unusual

00:31:26.767 --> 00:31:29.100
examples, you can end up creating rules

00:31:29.100 --> 00:31:31.410
based on those examples that don't

00:31:31.410 --> 00:31:32.920
generalize well tuning data.

00:31:33.640 --> 00:31:36.191
And so some things that you can do are

00:31:36.191 --> 00:31:38.119
you can stop Training, stop Training

00:31:38.120 --> 00:31:38.590
early.

00:31:38.590 --> 00:31:40.440
So you can say I'm not going to split

00:31:40.440 --> 00:31:42.530
once I only have 5 examples of my leaf

00:31:42.530 --> 00:31:43.990
node, I'm going to quit splitting and

00:31:43.990 --> 00:31:45.460
I'll just output my best guess.

00:31:46.520 --> 00:31:47.070


00:31:47.990 --> 00:31:49.240
There's also like.

00:31:52.250 --> 00:31:53.770
Probably on Tuesday.

00:31:53.770 --> 00:31:54.810
Actually, I'm going to talk about

00:31:54.810 --> 00:31:56.790
ensembles, which is ways of combining

00:31:56.790 --> 00:31:58.770
money trees, which is another way of

00:31:58.770 --> 00:31:59.840
getting rid of this problem.

00:32:01.360 --> 00:32:01.750
Question.

00:32:09.850 --> 00:32:11.190
That's a good question too.

00:32:11.190 --> 00:32:12.890
So the question is whether Decision

00:32:12.890 --> 00:32:14.500
trees are always binary.

00:32:14.500 --> 00:32:17.880
So like in this example, it's not

00:32:17.880 --> 00:32:21.640
binary, they're splitting like the

00:32:21.640 --> 00:32:23.250
Patrons is splitting based on three

00:32:23.250 --> 00:32:23.780
values.

00:32:24.510 --> 00:32:28.260
But typically they are binary.

00:32:28.260 --> 00:32:29.030
So if you're.

00:32:29.810 --> 00:32:32.277
If you're using continuous values, it

00:32:32.277 --> 00:32:32.535
will.

00:32:32.535 --> 00:32:34.410
It will almost always be binary,

00:32:34.410 --> 00:32:35.440
because you could.

00:32:35.440 --> 00:32:37.330
Even if you wanted to split continuous

00:32:37.330 --> 00:32:40.260
variables into many different chunks,

00:32:40.260 --> 00:32:42.350
you can do that through a sequence of

00:32:42.350 --> 00:32:43.380
binary decisions.

00:32:44.780 --> 00:32:47.620
In SK learn as well, their Decision

00:32:47.620 --> 00:32:50.160
trees cannot deal with like multi

00:32:50.160 --> 00:32:53.040
valued attributes and so you need to

00:32:53.040 --> 00:32:55.000
convert them into binary attributes in

00:32:55.000 --> 00:32:56.470
order to use sklearn.

00:32:57.350 --> 00:32:59.470
And I think often that's done as a

00:32:59.470 --> 00:33:01.590
design Decision, because otherwise like

00:33:01.590 --> 00:33:03.050
some features will be like

00:33:03.050 --> 00:33:04.780
intrinsically more powerful than other

00:33:04.780 --> 00:33:06.690
features if they create like more

00:33:06.690 --> 00:33:07.340
splits.

00:33:07.340 --> 00:33:09.160
So it can cause like a bias in your

00:33:09.160 --> 00:33:09.990
feature selection.

00:33:10.740 --> 00:33:12.990
So they don't have to be binary, but

00:33:12.990 --> 00:33:15.160
it's a common common setting.

00:33:21.880 --> 00:33:24.480
Alright, so the Training 4 Decision

00:33:24.480 --> 00:33:26.760
tree again without yet getting into the

00:33:26.760 --> 00:33:27.000
math.

00:33:27.710 --> 00:33:30.935
Is Recursively for each node in the

00:33:30.935 --> 00:33:32.590
tree, if the labels and the node are

00:33:32.590 --> 00:33:33.120
mixed.

00:33:33.120 --> 00:33:35.256
So to start with, we're at the of the

00:33:35.256 --> 00:33:38.030
tree and we have all this data, and so

00:33:38.030 --> 00:33:39.676
essentially there's just right now some

00:33:39.676 --> 00:33:41.025
probability that's a no, some

00:33:41.025 --> 00:33:41.950
probability that's an 784x1.

00:33:41.950 --> 00:33:43.900
Those probabilities are close to 5050.

00:33:45.530 --> 00:33:47.410
Then I'm going to choose some attribute

00:33:47.410 --> 00:33:50.020
and split the values based on the data

00:33:50.020 --> 00:33:51.200
that reaches that node.

00:33:52.310 --> 00:33:54.310
So here I Choose this attribute the

00:33:54.310 --> 00:33:55.430
tree I'm creating up there.

00:33:56.110 --> 00:33:58.060
X2 is less than .6.

00:34:00.630 --> 00:34:05.310
If it's less than .6 then I go down one

00:34:05.310 --> 00:34:07.067
branch and if it's greater than I go

00:34:07.067 --> 00:34:08.210
down the other branch.

00:34:08.210 --> 00:34:10.870
So now then I can now start making

00:34:10.870 --> 00:34:13.440
decisions separately about this region

00:34:13.440 --> 00:34:14.260
in this region.

00:34:15.910 --> 00:34:19.200
So then I Choose another node and I say

00:34:19.200 --> 00:34:21.660
if X1 is less than 7.

00:34:22.630 --> 00:34:24.360
So I create this split and this only

00:34:24.360 --> 00:34:25.490
pertains to the data.

00:34:25.490 --> 00:34:27.570
Now that came down the first node so

00:34:27.570 --> 00:34:28.989
it's this side of the data.

00:34:29.710 --> 00:34:31.292
So if it's over here, then it's a no,

00:34:31.292 --> 00:34:33.220
if it's over here, then it's an X and

00:34:33.220 --> 00:34:34.620
Now I don't need to create anymore

00:34:34.620 --> 00:34:36.690
Decision nodes for this whole region of

00:34:36.690 --> 00:34:38.870
space because I have perfect

00:34:38.870 --> 00:34:39.630
Classification.

00:34:40.760 --> 00:34:43.010
Then I go to my top side.

00:34:43.730 --> 00:34:45.390
And I can make another split.

00:34:45.390 --> 00:34:47.760
So here there's actually more than one

00:34:47.760 --> 00:34:48.015
choice.

00:34:48.015 --> 00:34:49.960
I think that's like kind of equally

00:34:49.960 --> 00:34:51.460
good, but.

00:34:51.570 --> 00:34:56.230
Again, say if X2 is less than .8, then

00:34:56.230 --> 00:34:57.960
it goes down here where I'm still

00:34:57.960 --> 00:34:58.250
unsure.

00:34:58.250 --> 00:35:00.080
If it's greater than eight, then it's

00:35:00.080 --> 00:35:00.980
definitely a red X.

00:35:03.260 --> 00:35:05.120
And then I can keep doing that until I

00:35:05.120 --> 00:35:07.190
finally have a perfect Classification

00:35:07.190 --> 00:35:08.030
in the training data.

00:35:08.810 --> 00:35:10.000
So that's the full tree.

00:35:11.070 --> 00:35:13.830
And if you could stop early, you could

00:35:13.830 --> 00:35:15.739
say I'm not going to go past like 3

00:35:15.740 --> 00:35:18.310
levels, or that I'm going to stop

00:35:18.310 --> 00:35:20.910
splitting once my leaf node doesn't

00:35:20.910 --> 00:35:23.210
have more than five examples.

00:35:39.470 --> 00:35:41.560
Well, the question was does the first

00:35:41.560 --> 00:35:42.320
split matter?

00:35:42.320 --> 00:35:43.929
So I guess there's two parts to that.

00:35:43.930 --> 00:35:45.880
One is that I will tell you how we do

00:35:45.880 --> 00:35:46.980
this computationally.

00:35:46.980 --> 00:35:48.780
So you try to greedily find like the

00:35:48.780 --> 00:35:49.900
best split every time.

00:35:50.990 --> 00:35:53.530
And the other thing is that finding the

00:35:53.530 --> 00:35:57.290
minimum size tree is like a

00:35:57.290 --> 00:35:59.540
computationally hard problem.

00:36:00.540 --> 00:36:01.766
So it's infeasible.

00:36:01.766 --> 00:36:04.530
So you end up with a greedy solution

00:36:04.530 --> 00:36:06.020
where for every node you're choosing

00:36:06.020 --> 00:36:08.200
the best split for that node.

00:36:08.200 --> 00:36:10.045
But that doesn't necessarily give you

00:36:10.045 --> 00:36:11.680
the shortest tree overall, because you

00:36:11.680 --> 00:36:13.020
don't know like what kinds of splits

00:36:13.020 --> 00:36:14.250
will be available to you later.

00:36:16.710 --> 00:36:19.050
So it does matter, but you have like

00:36:19.050 --> 00:36:20.630
there's an algorithm for doing it in a

00:36:20.630 --> 00:36:21.550
decent way, yeah.

00:36:55.320 --> 00:36:55.860


00:36:57.660 --> 00:36:59.080
There have well.

00:37:01.160 --> 00:37:02.650
How will you know that it will work for

00:37:02.650 --> 00:37:03.320
like new data?

00:37:05.000 --> 00:37:09.209
So basically if you want to know, you

00:37:09.210 --> 00:37:10.740
do always want to know, you always want

00:37:10.740 --> 00:37:12.420
to know, right, if you if the model

00:37:12.420 --> 00:37:13.620
that you learned is going to work for

00:37:13.620 --> 00:37:14.540
new data.

00:37:14.540 --> 00:37:16.370
And so that's why I typically you would

00:37:16.370 --> 00:37:18.030
carve off, if you have some Training

00:37:18.030 --> 00:37:19.800
set, you'd carve off a validation set.

00:37:20.450 --> 00:37:22.380
And you would train it say with like

00:37:22.380 --> 00:37:25.040
70% of the Training examples and test

00:37:25.040 --> 00:37:27.850
it on the 30% of the held out Samples?

00:37:28.530 --> 00:37:30.040
And then there was held out Samples

00:37:30.040 --> 00:37:32.170
will give you an estimate of how well

00:37:32.170 --> 00:37:33.260
your method works.

00:37:33.260 --> 00:37:35.250
And so then like if you find for

00:37:35.250 --> 00:37:37.626
example that I trained a full tree and

00:37:37.626 --> 00:37:39.850
of course I got like 0% Training error,

00:37:39.850 --> 00:37:41.850
but my Test error is like 40%.

00:37:42.590 --> 00:37:44.990
Then you would probably say maybe I

00:37:44.990 --> 00:37:46.803
should try Training a shorter tree and

00:37:46.803 --> 00:37:48.930
then you can like retrain it with some

00:37:48.930 --> 00:37:51.120
constraints and then test it again on

00:37:51.120 --> 00:37:52.755
your validation set and Choose like

00:37:52.755 --> 00:37:53.830
your Parameters that way.

00:37:54.860 --> 00:37:57.581
There's also I'll talk about most

00:37:57.581 --> 00:37:59.140
likely, most likely this.

00:37:59.140 --> 00:38:01.020
I was planning to do it Thursday, but

00:38:01.020 --> 00:38:02.187
I'll probably do it next Tuesday.

00:38:02.187 --> 00:38:04.580
I'll talk about ensembles, including

00:38:04.580 --> 00:38:06.622
random forests, and those are like kind

00:38:06.622 --> 00:38:09.150
of like brain dead always work methods

00:38:09.150 --> 00:38:11.080
that combine a lot of trees and are

00:38:11.080 --> 00:38:13.439
really reliable whether you have a lot

00:38:13.439 --> 00:38:16.087
of data or well, you kind of need data.

00:38:16.087 --> 00:38:17.665
But whether you have a lot of features

00:38:17.665 --> 00:38:19.850
or a little features, they always work.

00:38:20.480 --> 00:38:21.480
They always work pretty well.

00:38:23.820 --> 00:38:25.950
Right, so in prediction then you just

00:38:25.950 --> 00:38:27.560
basically descend the tree, so you

00:38:27.560 --> 00:38:29.920
check the conditions is tX2 greater

00:38:29.920 --> 00:38:32.370
than .6 blah blah blah blah blah until

00:38:32.370 --> 00:38:33.750
you find yourself in a leaf node.

00:38:34.380 --> 00:38:36.630
So for example, if I have this data

00:38:36.630 --> 00:38:38.500
point and I'm trying to classify it, I

00:38:38.500 --> 00:38:40.902
would end up following these rules down

00:38:40.902 --> 00:38:44.290
to down to the leaf node of.

00:38:45.960 --> 00:38:47.418
Yeah, like right over here, right?

00:38:47.418 --> 00:38:50.158
X2 is less than .6 and X1 is less than

00:38:50.158 --> 00:38:50.460
.7.

00:38:51.260 --> 00:38:52.740
And so that's going to be no.

00:38:53.860 --> 00:38:56.500
And if I am over here then I end up

00:38:56.500 --> 00:38:59.420
following going down to here to here.

00:39:00.480 --> 00:39:03.020
To here to here and I end up in this

00:39:03.020 --> 00:39:07.299
leaf node and so it's an X and it

00:39:07.300 --> 00:39:09.395
doesn't matter like where it falls in

00:39:09.395 --> 00:39:10.580
this part of the space.

00:39:10.580 --> 00:39:11.700
Usually this isn't like.

00:39:12.390 --> 00:39:13.770
Even something you necessarily

00:39:13.770 --> 00:39:15.520
visualize, but.

00:39:16.060 --> 00:39:18.025
But it's worth noting that even parts

00:39:18.025 --> 00:39:20.020
of your feature space that are kind of

00:39:20.020 --> 00:39:22.640
far away from any Example can still get

00:39:22.640 --> 00:39:24.360
classified by this Decision tree.

00:39:25.070 --> 00:39:27.670
And it's not necessarily the Nearest

00:39:27.670 --> 00:39:28.450
neighbor Decision.

00:39:28.450 --> 00:39:31.186
Like this star here is actually closer

00:39:31.186 --> 00:39:33.390
to the 784x1 than it is to the O's, but

00:39:33.390 --> 00:39:35.010
it would still be a no because it's on

00:39:35.010 --> 00:39:36.050
that side of the boundary.

00:39:40.650 --> 00:39:42.350
So the key question is, how do you

00:39:42.350 --> 00:39:45.810
choose what attribute to split and

00:39:45.810 --> 00:39:46.384
where to split?

00:39:46.384 --> 00:39:48.390
So how do you decide what test you're

00:39:48.390 --> 00:39:50.000
going to use for a given node?

00:39:50.920 --> 00:39:53.615
And so let's take this example.

00:39:53.615 --> 00:39:56.290
So here I've got some table of features

00:39:56.290 --> 00:39:57.180
and predictions.

00:39:58.020 --> 00:39:59.010
And if.

00:40:00.410 --> 00:40:02.280
And if I were to split, these are

00:40:02.280 --> 00:40:04.570
binary features so they just have two

00:40:04.570 --> 00:40:06.430
values T2 false I guess.

00:40:07.400 --> 00:40:07.940
If.

00:40:09.620 --> 00:40:12.440
If I split based on X1 and I go in One

00:40:12.440 --> 00:40:14.570
Direction, then it's all true.

00:40:15.200 --> 00:40:17.585
The prediction is true and if I go in

00:40:17.585 --> 00:40:19.920
the other direction then 3/4 of the

00:40:19.920 --> 00:40:21.080
time the prediction is false.

00:40:22.810 --> 00:40:26.343
If I split based on X2, then 3/4 of the

00:40:26.343 --> 00:40:27.948
time the prediction is true.

00:40:27.948 --> 00:40:31.096
If it's true and 50% of the time the

00:40:31.096 --> 00:40:32.819
prediction is false, X2 is false.

00:40:33.530 --> 00:40:36.300
So which of these features is a better

00:40:36.300 --> 00:40:37.400
Test?

00:40:39.550 --> 00:40:41.530
So how many people think that the left

00:40:41.530 --> 00:40:42.530
is a better Test?

00:40:43.790 --> 00:40:45.070
How many people think they're right is

00:40:45.070 --> 00:40:45.730
a better Test.

00:40:46.840 --> 00:40:48.380
Right the left is a better Test

00:40:48.380 --> 00:40:48.950
because.

00:40:50.620 --> 00:40:53.380
Because my uncertainty is greatly

00:40:53.380 --> 00:40:54.990
reduced on the left side.

00:40:54.990 --> 00:40:58.750
So initially, initially I had like a

00:40:58.750 --> 00:41:01.280
5/8 chance of getting it right if I

00:41:01.280 --> 00:41:02.280
just guessed true.

00:41:02.910 --> 00:41:06.706
But if I know X1, then I've got a 100%

00:41:06.706 --> 00:41:08.600
chance of getting it right, at least in

00:41:08.600 --> 00:41:09.494
the training data.

00:41:09.494 --> 00:41:13.338
If I know that X1 is true, and I've got

00:41:13.338 --> 00:41:15.132
a 3/4 chance of getting it right if I

00:41:15.132 --> 00:41:16.280
know that X1 is false.

00:41:16.280 --> 00:41:19.135
So X1 tells me a lot about the

00:41:19.135 --> 00:41:19.572
prediction.

00:41:19.572 --> 00:41:22.035
It greatly reduces my uncertainty about

00:41:22.035 --> 00:41:22.890
the prediction.

00:41:24.510 --> 00:41:26.412
And to quantify this, we need to

00:41:26.412 --> 00:41:28.560
quantify uncertainty and then be able

00:41:28.560 --> 00:41:32.350
to measure how much a certain feature

00:41:32.350 --> 00:41:33.950
reduces our uncertainty in the

00:41:33.950 --> 00:41:34.720
prediction.

00:41:34.720 --> 00:41:36.800
And that's called the information gain.

00:41:40.470 --> 00:41:44.540
So to quantify the uncertainty, I'll

00:41:44.540 --> 00:41:45.595
use these two examples.

00:41:45.595 --> 00:41:47.790
So imagine that you're flipping a coin.

00:41:47.790 --> 00:41:50.150
These are like heads and tails, or

00:41:50.150 --> 00:41:51.510
present them as zeros and ones.

00:41:52.180 --> 00:41:54.820
And so one time I've got two different

00:41:54.820 --> 00:41:56.186
sequences, let's say two different

00:41:56.186 --> 00:41:57.740
coins and one in the coins.

00:41:57.740 --> 00:42:00.120
It's a biased coin, so I end up with

00:42:00.120 --> 00:42:03.330
zeros or heads like 16 out of 18 times.

00:42:04.250 --> 00:42:06.520
And the other for the other Coin I get

00:42:06.520 --> 00:42:09.400
closer to 5058 out of.

00:42:10.050 --> 00:42:12.390
18 times I get heads so.

00:42:13.530 --> 00:42:17.520
Which of these has higher uncertainty?

00:42:18.540 --> 00:42:19.730
The left or the right?

00:42:21.330 --> 00:42:22.580
Right, correct.

00:42:22.580 --> 00:42:23.070
They're right.

00:42:23.070 --> 00:42:24.900
Has a lot higher uncertainty.

00:42:24.900 --> 00:42:27.370
So if I with that Coin, I really don't

00:42:27.370 --> 00:42:28.470
know if it's going to be heads or

00:42:28.470 --> 00:42:30.860
tails, but on the left side, I'm pretty

00:42:30.860 --> 00:42:31.820
sure it's going to be heads.

00:42:32.590 --> 00:42:33.360
Or zeros.

00:42:34.720 --> 00:42:36.770
So we can measure that with this

00:42:36.770 --> 00:42:38.645
function called Entropy.

00:42:38.645 --> 00:42:41.350
So the entropy is a measure of

00:42:41.350 --> 00:42:42.030
uncertainty.

00:42:42.960 --> 00:42:45.740
And it's defined as the negative sum

00:42:45.740 --> 00:42:48.070
over all the values of some variable of

00:42:48.070 --> 00:42:50.220
the probability of that value.

00:42:51.020 --> 00:42:53.490
Times the log probability that value,

00:42:53.490 --> 00:42:56.470
and people usually sometimes use like

00:42:56.470 --> 00:42:57.520
log base 2.

00:42:58.630 --> 00:43:00.700
Just because that way the Entropy

00:43:00.700 --> 00:43:02.550
ranges from zero to 1 if you have

00:43:02.550 --> 00:43:03.490
binary variables.

00:43:07.600 --> 00:43:10.820
So for this case here, the Entropy

00:43:10.820 --> 00:43:13.280
would be -, 8 ninths, because eight out

00:43:13.280 --> 00:43:14.600
of nine times it's zero.

00:43:15.270 --> 00:43:17.300
Times log two of eight ninths.

00:43:18.230 --> 00:43:21.210
Minus one ninth times, log 2 of 1 ninth

00:43:21.210 --> 00:43:22.790
and that works out to about 1/2.

00:43:24.370 --> 00:43:28.480
And over here the Entropy is -, 4

00:43:28.480 --> 00:43:30.270
ninths because four out of nine times,

00:43:30.270 --> 00:43:32.900
or 8 out of 18 times, it's a 0.

00:43:34.410 --> 00:43:37.104
Times log 24 ninths, minus five ninths,

00:43:37.104 --> 00:43:39.010
times log two of five ninths, and

00:43:39.010 --> 00:43:41.490
that's about 99.

00:43:43.430 --> 00:43:45.280
The Entropy measure is how surprised

00:43:45.280 --> 00:43:47.595
are we by some new value of this

00:43:47.595 --> 00:43:47.830
Sequence?

00:43:47.830 --> 00:43:50.123
How surprised are we likely to be in,

00:43:50.123 --> 00:43:52.460
or how much information does it convey

00:43:52.460 --> 00:43:54.895
that we know that we're in this

00:43:54.895 --> 00:43:56.974
Sequence, or more generally, that we

00:43:56.974 --> 00:43:57.940
know some feature?

00:44:01.100 --> 00:44:03.425
So this is just showing the Entropy if

00:44:03.425 --> 00:44:05.450
the probability if you have a binary

00:44:05.450 --> 00:44:06.340
variable X.

00:44:07.110 --> 00:44:09.720
And the probability of X is 0, then

00:44:09.720 --> 00:44:12.180
your Entropy is 0 because you always

00:44:12.180 --> 00:44:15.127
know that if probability of X = 2 is

00:44:15.127 --> 00:44:16.818
zero, that means that probability of X

00:44:16.818 --> 00:44:18.210
equals false is 1.

00:44:18.860 --> 00:44:20.530
And so therefore you have complete

00:44:20.530 --> 00:44:22.470
confidence that the value will be

00:44:22.470 --> 00:44:22.810
false.

00:44:24.070 --> 00:44:27.740
If probability of X is true is 1, then

00:44:27.740 --> 00:44:29.590
you have complete confidence that the

00:44:29.590 --> 00:44:30.650
value will be true.

00:44:31.440 --> 00:44:35.570
But if it's .5, then you have no

00:44:35.570 --> 00:44:37.120
information about whether it's true or

00:44:37.120 --> 00:44:39.520
false, and so you have maximum entropy,

00:44:39.520 --> 00:44:40.190
which is 1.

00:44:45.770 --> 00:44:47.280
So here's another example.

00:44:47.280 --> 00:44:49.340
So suppose that we've got two

00:44:49.340 --> 00:44:51.070
variables, whether it's raining or not,

00:44:51.070 --> 00:44:52.220
and whether it's cloudy or not.

00:44:52.820 --> 00:44:55.700
And we've observed 100 days and marked

00:44:55.700 --> 00:44:57.260
down whether it's rainy or cloudy.

00:44:58.870 --> 00:45:00.150
Many and or Cloudy.

00:45:00.930 --> 00:45:01.500


00:45:02.600 --> 00:45:06.300
So 24 days it was raining and cloudy.

00:45:06.300 --> 00:45:08.210
One day it was raining and not Cloudy.

00:45:09.320 --> 00:45:11.244
25 days it was not raining and cloudy

00:45:11.244 --> 00:45:13.409
and 50 days it was not raining and not

00:45:13.409 --> 00:45:13.649
Cloudy.

00:45:15.620 --> 00:45:17.980
The probabilities are just dividing by

00:45:17.980 --> 00:45:18.766
the total there.

00:45:18.766 --> 00:45:20.850
So the probability of Cloudy and not

00:45:20.850 --> 00:45:22.630
raining is 25 out of 100.

00:45:24.040 --> 00:45:26.660
And so I can also compute an Entropy of

00:45:26.660 --> 00:45:27.855
this whole joint distribution.

00:45:27.855 --> 00:45:31.150
So I can say that the entropy of X&Y

00:45:31.150 --> 00:45:33.446
together is the sum all the different

00:45:33.446 --> 00:45:35.428
values of X and the over all the

00:45:35.428 --> 00:45:36.419
different values of Y.

00:45:37.060 --> 00:45:39.770
Of probability of X&Y times log 2,

00:45:39.770 --> 00:45:41.920
probability of X&Y, and then that's all

00:45:41.920 --> 00:45:42.880
just like written out here.

00:45:43.650 --> 00:45:45.115
And then I get some Entropy value.

00:45:45.115 --> 00:45:47.940
And sometimes people call those units

00:45:47.940 --> 00:45:51.490
bits, so 156 bits because that's the

00:45:51.490 --> 00:45:53.008
amount of, that's the number of bits

00:45:53.008 --> 00:45:54.680
that I would need that I would expect

00:45:54.680 --> 00:45:55.040
to.

00:45:55.790 --> 00:45:57.780
Be able to like represent this.

00:45:58.630 --> 00:45:59.700
This information.

00:46:00.430 --> 00:46:04.395
If you if it were always not Cloudy and

00:46:04.395 --> 00:46:04.990
not raining.

00:46:05.850 --> 00:46:08.020
If it were 100% of the time not Cloudy

00:46:08.020 --> 00:46:10.280
and not raining, then you'd have 0 bits

00:46:10.280 --> 00:46:11.830
because you don't need any data to

00:46:11.830 --> 00:46:12.810
represent the.

00:46:13.710 --> 00:46:15.770
That uncertainty, it's just always

00:46:15.770 --> 00:46:16.300
true.

00:46:16.300 --> 00:46:18.300
I mean it's always like one value.

00:46:18.300 --> 00:46:20.790
So 15 bits means that you have pretty

00:46:20.790 --> 00:46:21.490
high uncertainty.

00:46:25.250 --> 00:46:27.680
There's also a concept called specific

00:46:27.680 --> 00:46:28.510
Entropy.

00:46:28.510 --> 00:46:29.780
So that is.

00:46:29.780 --> 00:46:33.560
That means that if one thing, then how

00:46:33.560 --> 00:46:34.516
much does that?

00:46:34.516 --> 00:46:36.610
How much uncertainty do you have left?

00:46:37.460 --> 00:46:41.170
So, for example, what is the entropy of

00:46:41.170 --> 00:46:43.610
cloudiness given that I know that it's

00:46:43.610 --> 00:46:44.000
raining?

00:46:45.420 --> 00:46:48.940
And the Conditional Entropy is very

00:46:48.940 --> 00:46:51.280
similar form, it's just negative sum

00:46:51.280 --> 00:46:52.720
over the values of the.

00:46:53.710 --> 00:46:54.970
The thing that you're measuring the

00:46:54.970 --> 00:46:55.780
Entropy over.

00:46:56.800 --> 00:46:58.880
The probability of that given the thing

00:46:58.880 --> 00:46:59.500
that.

00:47:00.150 --> 00:47:03.610
Times the log probability of Y given X,

00:47:03.610 --> 00:47:04.760
where Y is the thing you're measuring

00:47:04.760 --> 00:47:06.400
the uncertainty of, and X is a thing

00:47:06.400 --> 00:47:06.850
that you know.

00:47:09.200 --> 00:47:12.660
So if I know that it's Cloudy, then

00:47:12.660 --> 00:47:15.690
there's a 24 out of 25 chance that

00:47:15.690 --> 00:47:16.150
it's.

00:47:17.340 --> 00:47:17.950
Wait, no.

00:47:17.950 --> 00:47:19.910
If I know that it's raining, sorry.

00:47:19.910 --> 00:47:21.599
If I know that it's raining, then

00:47:21.600 --> 00:47:23.931
there's a 24 out of 25 chance that it's

00:47:23.931 --> 00:47:24.430
Cloudy, right?

00:47:24.430 --> 00:47:26.190
And then one out of 25 chance that it's

00:47:26.190 --> 00:47:26.760
not Cloudy.

00:47:27.600 --> 00:47:30.340
So I get 24 to 25 there and one out of

00:47:30.340 --> 00:47:33.070
25 there, and now my Entropy is greatly

00:47:33.070 --> 00:47:33.660
reduced.

00:47:39.810 --> 00:47:41.280
And then you can also measure.

00:47:41.930 --> 00:47:44.250
In expected Conditional Entropy.

00:47:46.020 --> 00:47:50.570
So that's just the probability of.

00:47:50.570 --> 00:47:53.870
That's just taking the specific

00:47:53.870 --> 00:47:54.940
Conditional Entropy.

00:47:55.780 --> 00:47:58.660
At times the probability of each of the

00:47:58.660 --> 00:48:00.360
values that I might know.

00:48:01.260 --> 00:48:03.710
Summed up over the different values,

00:48:03.710 --> 00:48:04.180
so.

00:48:04.900 --> 00:48:06.130
The.

00:48:06.820 --> 00:48:09.920
The expected Conditional value Entropy

00:48:09.920 --> 00:48:11.950
for knowing whether or not it's raining

00:48:11.950 --> 00:48:15.179
would be the Conditional Entropy.

00:48:16.040 --> 00:48:19.010
Of it raining if I know it's raining.

00:48:19.920 --> 00:48:21.280
Times the probability that it's

00:48:21.280 --> 00:48:21.720
raining.

00:48:22.460 --> 00:48:24.460
Plus the.

00:48:25.190 --> 00:48:28.270
Entropy of cloudiness given that it's

00:48:28.270 --> 00:48:30.210
not raining, times the probability

00:48:30.210 --> 00:48:30.900
that's not raining.

00:48:33.530 --> 00:48:35.550
And that's also equal to this thing.

00:48:42.960 --> 00:48:43.400
Right.

00:48:43.400 --> 00:48:46.168
So if I want to know what is the

00:48:46.168 --> 00:48:47.790
entropy of cloudiness, I guess I said

00:48:47.790 --> 00:48:48.730
it a little early.

00:48:48.730 --> 00:48:50.890
What is the entropy of cloudiness given

00:48:50.890 --> 00:48:52.720
whether that we know whether or not

00:48:52.720 --> 00:48:53.340
it's raining?

00:48:54.310 --> 00:48:56.240
Then that is.

00:48:56.850 --> 00:48:59.540
Going to be like 1/4, which is the

00:48:59.540 --> 00:49:02.009
probability that it's raining, is that

00:49:02.010 --> 00:49:02.320
right?

00:49:02.320 --> 00:49:04.790
25 out of 100 times it's raining.

00:49:05.490 --> 00:49:08.225
So 1/4 is the probability that it's

00:49:08.225 --> 00:49:11.240
raining times the Entropy of cloudiness

00:49:11.240 --> 00:49:13.840
given that it's raining plus three

00:49:13.840 --> 00:49:15.710
quarter times it's not raining times

00:49:15.710 --> 00:49:17.570
the entropy of the cloudiness given

00:49:17.570 --> 00:49:18.810
that it's not raining.

00:49:20.470 --> 00:49:23.420
So that's a measure of how much does

00:49:23.420 --> 00:49:25.930
knowing whether or not it's rainy, or

00:49:25.930 --> 00:49:28.470
how much uncertainty do I have left if

00:49:28.470 --> 00:49:29.880
I know whether or not it's raining.

00:49:32.430 --> 00:49:34.030
How much do I expect to have left?

00:49:37.700 --> 00:49:39.800
So some useful things to know is that

00:49:39.800 --> 00:49:41.585
the Entropy is always nonnegative.

00:49:41.585 --> 00:49:43.580
You can never have negative Entropy,

00:49:43.580 --> 00:49:45.410
but do make sure you remember.

00:49:46.480 --> 00:49:47.310


00:49:48.750 --> 00:49:50.380
So do make sure you remember these

00:49:50.380 --> 00:49:53.390
negative signs in this like

00:49:53.390 --> 00:49:54.910
probability, otherwise if you end up

00:49:54.910 --> 00:49:56.780
with a negative Entropy that you left

00:49:56.780 --> 00:49:57.490
something out.

00:49:59.760 --> 00:50:02.815
You also have this chain rule, so the

00:50:02.815 --> 00:50:06.320
entropy X&Y is the entropy of X given Y

00:50:06.320 --> 00:50:08.580
plus the entropy of Y, which kind of

00:50:08.580 --> 00:50:10.260
makes sense because the Entropy of

00:50:10.260 --> 00:50:11.280
knowing two things.

00:50:12.310 --> 00:50:14.540
Of the values of two things, is the

00:50:14.540 --> 00:50:15.914
value of knowing one.

00:50:15.914 --> 00:50:18.785
Is the OR sorry, the Entropy or the

00:50:18.785 --> 00:50:20.199
uncertainty of knowing two things?

00:50:20.199 --> 00:50:22.179
Is the uncertainty of knowing one of

00:50:22.180 --> 00:50:22.580
them?

00:50:23.280 --> 00:50:24.940
Plus the uncertainty of knowing the

00:50:24.940 --> 00:50:26.515
other one, given that you already know

00:50:26.515 --> 00:50:27.350
One South.

00:50:27.350 --> 00:50:30.169
It's either Entropy of X given Y plus

00:50:30.169 --> 00:50:32.323
Entropy of Y, or Entropy of Y given X

00:50:32.323 --> 00:50:33.250
plus Entropy of 784x1.

00:50:34.640 --> 00:50:38.739
X&Y are independent, then Entropy of Y

00:50:38.740 --> 00:50:40.659
given X is equal the entropy of Y.

00:50:42.870 --> 00:50:44.520
Meaning that 784X1 doesn't reduce our

00:50:44.520 --> 00:50:45.240
uncertainty at all.

00:50:46.530 --> 00:50:48.845
And Entropy of anything with itself is

00:50:48.845 --> 00:50:50.330
0, because once you know it, then

00:50:50.330 --> 00:50:51.480
there's no uncertainty anymore.

00:50:52.880 --> 00:50:53.390
And then?

00:50:54.110 --> 00:50:57.970
If you do know something, Entropy of Y

00:50:57.970 --> 00:50:59.780
given X or at least has to be less than

00:50:59.780 --> 00:51:01.430
or equal the entropy of Y.

00:51:01.430 --> 00:51:04.020
So knowing something can never increase

00:51:04.020 --> 00:51:04.690
your uncertainty.

00:51:07.660 --> 00:51:09.520
So then finally we can get to this

00:51:09.520 --> 00:51:11.132
information gain.

00:51:11.132 --> 00:51:14.730
So information gain is the change in

00:51:14.730 --> 00:51:17.530
the Entropy due to learning something

00:51:17.530 --> 00:51:17.810
new.

00:51:20.100 --> 00:51:23.310
So I can say, for example, what is?

00:51:23.310 --> 00:51:26.160
How much does knowing whether or not

00:51:26.160 --> 00:51:27.010
it's rainy?

00:51:27.960 --> 00:51:30.610
Reduce my uncertainty of cloudiness.

00:51:31.620 --> 00:51:34.542
So that would be the Entropy of

00:51:34.542 --> 00:51:37.242
cloudiness minus the entropy of

00:51:37.242 --> 00:51:39.120
cloudiness given whether or not it's

00:51:39.120 --> 00:51:39.450
raining.

00:51:41.710 --> 00:51:43.990
So that's the Entropy of cloudiness

00:51:43.990 --> 00:51:46.500
minus the entropy of cloudiness given

00:51:46.500 --> 00:51:47.640
whether it's raining.

00:51:47.640 --> 00:51:49.660
And that's 25 bits.

00:51:49.660 --> 00:51:50.993
So that's like the value.

00:51:50.993 --> 00:51:52.860
It's essentially the value of knowing

00:51:52.860 --> 00:51:54.100
whether or not it's meaning.

00:51:59.210 --> 00:52:01.140
And then finally we can use this in our

00:52:01.140 --> 00:52:02.140
Decision tree.

00:52:02.140 --> 00:52:03.660
So if we recall.

00:52:04.300 --> 00:52:07.310
The Decision tree algorithm is that.

00:52:08.410 --> 00:52:10.940
If I'm trying to I go through like

00:52:10.940 --> 00:52:12.700
splitting my data.

00:52:13.550 --> 00:52:15.050
Choose some Test.

00:52:15.050 --> 00:52:17.280
According to the test, I split the data

00:52:17.280 --> 00:52:18.970
into different nodes and then I choose

00:52:18.970 --> 00:52:20.440
a new test for each of those nodes.

00:52:21.440 --> 00:52:22.840
So the key thing we're trying to figure

00:52:22.840 --> 00:52:24.007
out is how do we do that Test?

00:52:24.007 --> 00:52:25.800
How do we choose the features or

00:52:25.800 --> 00:52:27.480
attributes and the splitting value?

00:52:28.370 --> 00:52:30.100
To try to split things into different

00:52:30.100 --> 00:52:32.030
classes, or in other words, to try to

00:52:32.030 --> 00:52:33.640
reduce the uncertainty of our

00:52:33.640 --> 00:52:34.150
prediction.

00:52:36.190 --> 00:52:39.790
And the solution is to choose the

00:52:39.790 --> 00:52:42.450
attribute to choose the Test that

00:52:42.450 --> 00:52:44.780
maximizes the information gain.

00:52:44.780 --> 00:52:46.770
In other words, that reduces the

00:52:46.770 --> 00:52:49.600
entropy of the most for the current

00:52:49.600 --> 00:52:50.370
data in that node.

00:52:52.000 --> 00:52:52.530
So.

00:52:53.260 --> 00:52:56.478
What you would do is for each for each

00:52:56.478 --> 00:52:58.700
discrete attribute or discrete feature.

00:52:59.630 --> 00:53:02.063
You can compute the information gain of

00:53:02.063 --> 00:53:04.140
using that using that feature.

00:53:04.140 --> 00:53:06.620
So in the case of.

00:53:07.360 --> 00:53:08.280
Go back a bit.

00:53:09.010 --> 00:53:11.670
To this simple true false all right, so

00:53:11.670 --> 00:53:12.650
for example.

00:53:13.650 --> 00:53:15.520
Here I started out with a pretty high

00:53:15.520 --> 00:53:17.550
Entropy, close to one because 5/8 of

00:53:17.550 --> 00:53:18.050
the time.

00:53:18.690 --> 00:53:20.850
The value of Y is true and three it's

00:53:20.850 --> 00:53:21.180
false.

00:53:22.030 --> 00:53:26.620
And so I can say for X1, what's my

00:53:26.620 --> 00:53:28.970
Entropy after X1?

00:53:28.970 --> 00:53:31.020
It's a 5050 chance that it goes either

00:53:31.020 --> 00:53:31.313
way.

00:53:31.313 --> 00:53:34.020
So this will be 50 * 0 because the

00:53:34.020 --> 00:53:36.541
Entropy here is 0 and this will be 50

00:53:36.541 --> 00:53:36.815
times.

00:53:36.815 --> 00:53:38.630
I don't know, one or something,

00:53:38.630 --> 00:53:40.659
whatever that Entropy is, and so this

00:53:40.659 --> 00:53:42.100
Entropy will be really low.

00:53:43.000 --> 00:53:45.700
And this Entropy is just about as high

00:53:45.700 --> 00:53:46.590
as I started with.

00:53:46.590 --> 00:53:48.330
It's only a little bit lower maybe

00:53:48.330 --> 00:53:50.510
because if I go this way, I have

00:53:50.510 --> 00:53:52.691
Entropy of 1, there's a 50% chance of

00:53:52.691 --> 00:53:55.188
that, and if I go this way, then I have

00:53:55.188 --> 00:53:56.721
lower Entropy and there's a 50% chance

00:53:56.721 --> 00:53:57.159
of that.

00:53:57.870 --> 00:54:00.010
And so my information gain is my

00:54:00.010 --> 00:54:01.600
initial entropy of Y.

00:54:02.980 --> 00:54:06.550
Minus the entropy of each of these, and

00:54:06.550 --> 00:54:08.005
here the Entropy gain.

00:54:08.005 --> 00:54:10.210
The information gain of X1 is much

00:54:10.210 --> 00:54:12.940
lower than X2 and so I Choose X1.

00:54:18.810 --> 00:54:20.420
So if I have discrete values, I just

00:54:20.420 --> 00:54:22.449
compute the information gain for the

00:54:22.450 --> 00:54:24.290
current node for each of those discrete

00:54:24.290 --> 00:54:25.725
values, and then I choose the one with

00:54:25.725 --> 00:54:26.860
the highest information gain.

00:54:27.780 --> 00:54:29.650
If I have continuous values, it's

00:54:29.650 --> 00:54:31.576
slightly more complicated because then

00:54:31.576 --> 00:54:34.395
I have to also choose a threshold in

00:54:34.395 --> 00:54:36.230
the lemons and.

00:54:36.920 --> 00:54:40.150
And oranges we were choosing saying if

00:54:40.150 --> 00:54:42.010
the height is greater than six then we

00:54:42.010 --> 00:54:42.620
go one way.

00:54:44.560 --> 00:54:46.640
So we have to choose which feature and

00:54:46.640 --> 00:54:47.420
which threshold.

00:54:48.430 --> 00:54:49.580
So typically.

00:54:51.060 --> 00:54:53.512
Something this I don't know.

00:54:53.512 --> 00:54:56.295
Like who thought putting a projector in

00:54:56.295 --> 00:54:57.930
a jewel would be like a nice way to?

00:54:58.590 --> 00:55:00.260
Right and stuff, but anyway.

00:55:04.700 --> 00:55:06.340
But at least it's something, all right?

00:55:06.340 --> 00:55:08.400
So let's say that I have some feature.

00:55:09.420 --> 00:55:11.910
And I've got like some different

00:55:11.910 --> 00:55:13.240
classes and that feature.

00:55:16.190 --> 00:55:18.560
So what I would do is I would usually

00:55:18.560 --> 00:55:19.950
you would sort the values.

00:55:20.890 --> 00:55:22.440
And you're never going to want to split

00:55:22.440 --> 00:55:24.010
between two of the same class, so I

00:55:24.010 --> 00:55:26.469
would never split between the two X's,

00:55:26.470 --> 00:55:29.250
because that's always going to be worse

00:55:29.250 --> 00:55:31.070
than some split that's between

00:55:31.070 --> 00:55:31.930
different classes.

00:55:32.630 --> 00:55:35.450
So I can consider the thresholds that

00:55:35.450 --> 00:55:35.810
are.

00:55:36.460 --> 00:55:37.730
Between different classes.

00:55:42.380 --> 00:55:44.000
Really.

00:55:44.000 --> 00:55:44.530
No.

00:55:46.130 --> 00:55:48.380
Yeah, I can, but I'm not going to draw

00:55:48.380 --> 00:55:50.220
that long, so it's not worth it to me

00:55:50.220 --> 00:55:50.860
to move on here.

00:55:50.860 --> 00:55:52.160
Then I have to move my laptop and.

00:55:53.030 --> 00:55:56.030
So I'm fine.

00:55:56.750 --> 00:55:59.310
So I would choose these two thresholds.

00:55:59.310 --> 00:56:01.680
If it's this threshold, then it's

00:56:01.680 --> 00:56:04.152
basically two and zero.

00:56:04.152 --> 00:56:07.470
So it's a very low Entropy here.

00:56:07.470 --> 00:56:10.420
And the probability of that is 2 out of

00:56:10.420 --> 00:56:11.505
five, right?

00:56:11.505 --> 00:56:16.820
So it would be 0.4 * 0 is the.

00:56:17.460 --> 00:56:18.580
Entropy on this side.

00:56:19.570 --> 00:56:20.820
And if I go this way?

00:56:21.670 --> 00:56:23.500
Then it's going to be.

00:56:24.440 --> 00:56:25.290
Then I've got.

00:56:26.660 --> 00:56:27.840
Sorry, two out of seven.

00:56:29.750 --> 00:56:31.320
Out of seven times.

00:56:32.470 --> 00:56:33.930
Times Entropy of 0 this way.

00:56:34.650 --> 00:56:37.630
And if I go this way, then it's five

00:56:37.630 --> 00:56:38.020
out of.

00:56:38.980 --> 00:56:39.760
7.

00:56:41.040 --> 00:56:41.770
Times.

00:56:44.510 --> 00:56:47.560
Two out of five times log.

00:56:52.980 --> 00:56:53.690
Thank you.

00:56:53.690 --> 00:56:55.330
I always forget the minus sign.

00:56:56.140 --> 00:56:58.270
OK, so minus 5 to 7, which is a

00:56:58.270 --> 00:56:59.880
probability that I go in this direction

00:56:59.880 --> 00:57:03.805
times one out of five times log one out

00:57:03.805 --> 00:57:04.700
of five.

00:57:05.550 --> 00:57:07.760
Plus four out of five.

00:57:09.170 --> 00:57:10.710
Four to five times log.

00:57:13.360 --> 00:57:14.100
Right.

00:57:14.100 --> 00:57:15.750
So there's a one fifth chance that it's

00:57:15.750 --> 00:57:16.270
an X.

00:57:17.350 --> 00:57:19.180
I do 1/5 times log 1/5.

00:57:19.820 --> 00:57:22.200
Minus 4/5 chance that it's a no, so

00:57:22.200 --> 00:57:23.790
minus 4/5 times log four fifth.

00:57:24.510 --> 00:57:26.210
And this whole thing is the Entropy

00:57:26.210 --> 00:57:27.140
after that split.

00:57:28.590 --> 00:57:30.650
And then likewise I can evaluate this

00:57:30.650 --> 00:57:32.850
split as well and so.

00:57:33.620 --> 00:57:35.650
Out of these two splits, which one do

00:57:35.650 --> 00:57:37.190
you think will have the most

00:57:37.190 --> 00:57:38.040
information gain?

00:57:41.220 --> 00:57:43.320
Yeah, the left split, the first one has

00:57:43.320 --> 00:57:45.050
the most information gain because then

00:57:45.050 --> 00:57:47.168
I get a confident Decision about two

00:57:47.168 --> 00:57:49.943
X's and like 4 out of five chance of

00:57:49.943 --> 00:57:51.739
getting it right on the other side,

00:57:51.740 --> 00:57:53.520
where if I choose the right split, I

00:57:53.520 --> 00:57:56.791
only get a perfect confidence about 1X

00:57:56.791 --> 00:57:59.529
and A2 out of three chance of getting

00:57:59.529 --> 00:58:00.529
it right on the other side.

00:58:15.920 --> 00:58:19.580
OK, so if I continuous features I would

00:58:19.580 --> 00:58:21.490
just try all the different like

00:58:21.490 --> 00:58:23.110
candidate thresholds for all those

00:58:23.110 --> 00:58:24.690
features and then choose the best one.

00:58:26.430 --> 00:58:28.360
And.

00:58:28.460 --> 00:58:29.720
She's the best one, all right.

00:58:29.720 --> 00:58:30.090
That's it.

00:58:30.090 --> 00:58:31.430
And then I do that for all the nodes,

00:58:31.430 --> 00:58:32.590
then I do it Recursively.

00:58:33.670 --> 00:58:35.660
So if you have a lot of features and a

00:58:35.660 --> 00:58:37.050
lot of data, this can kind of take a

00:58:37.050 --> 00:58:37.600
long time.

00:58:38.250 --> 00:58:40.610
But I mean these operations are super

00:58:40.610 --> 00:58:41.710
fast so.

00:58:42.980 --> 00:58:45.919
In practice, when you run it so in

00:58:45.920 --> 00:58:48.380
homework two, I'll have you train tree

00:58:48.380 --> 00:58:50.930
train forests of Decision trees, where

00:58:50.930 --> 00:58:54.165
you train 100 of them for example, and

00:58:54.165 --> 00:58:56.090
it takes like a few seconds, so it's

00:58:56.090 --> 00:58:57.204
like pretty fast.

00:58:57.204 --> 00:58:59.070
These are these are actually not that

00:58:59.070 --> 00:59:01.030
computationally expensive, even though

00:59:01.030 --> 00:59:02.610
doing it manually would take forever.

00:59:05.590 --> 00:59:06.980
So.

00:59:08.860 --> 00:59:10.970
We're close to the we're close to the

00:59:10.970 --> 00:59:11.690
end of the lecture.

00:59:12.320 --> 00:59:14.320
But I will give you just a second to

00:59:14.320 --> 00:59:15.230
catch your breath.

00:59:15.230 --> 00:59:17.030
And while you're doing that, think

00:59:17.030 --> 00:59:17.690
about.

00:59:19.060 --> 00:59:22.640
If I were to try and in this case I'm

00:59:22.640 --> 00:59:23.760
showing like all the different

00:59:23.760 --> 00:59:25.210
examples, the numbers are different

00:59:25.210 --> 00:59:27.530
examples there and the color is whether

00:59:27.530 --> 00:59:28.270
they wait or not.

00:59:28.850 --> 00:59:30.570
And I'm trying to decide whether I'm

00:59:30.570 --> 00:59:33.090
going to make a decision based on the

00:59:33.090 --> 00:59:35.096
type of restaurant or based on whether

00:59:35.096 --> 00:59:35.860
the restaurant's full.

00:59:36.490 --> 00:59:40.840
So take a moment to stretch or zone

00:59:40.840 --> 00:59:42.760
out, and then I'll ask you what the

00:59:42.760 --> 00:59:43.200
answer is.

01:00:05.270 --> 01:00:06.606
Part of it, yeah.

01:00:06.606 --> 01:00:08.755
So this is all Training one tree.

01:00:08.755 --> 01:00:10.840
And for a random forest you just

01:00:10.840 --> 01:00:14.246
randomly sample features and randomly

01:00:14.246 --> 01:00:16.760
sample data, and then you train a tree

01:00:16.760 --> 01:00:19.250
and then you do that like N times and

01:00:19.250 --> 01:00:20.600
then you average the predictions.

01:00:27.420 --> 01:00:27.810
Yeah.

01:00:30.860 --> 01:00:33.610
And so essentially, since the previous

01:00:33.610 --> 01:00:35.440
Entropy is fixed when you're trying to

01:00:35.440 --> 01:00:36.140
make a decision.

01:00:36.910 --> 01:00:38.739
You're just essentially choosing the

01:00:38.740 --> 01:00:41.810
Decision, choosing the attribute that

01:00:41.810 --> 01:00:45.320
will minimize your expected Entropy

01:00:45.320 --> 01:00:47.160
after, like given that attribute.

01:00:57.950 --> 01:01:00.790
Alright, so how many people think that

01:01:00.790 --> 01:01:02.610
we should split?

01:01:03.300 --> 01:01:04.710
How many people think we should split

01:01:04.710 --> 01:01:05.580
based on type?

01:01:08.180 --> 01:01:09.580
How many people think we should split

01:01:09.580 --> 01:01:10.520
based on Patrons?

01:01:12.730 --> 01:01:13.680
Yeah, OK.

01:01:14.430 --> 01:01:17.380
So I would say the answer is Patrons

01:01:17.380 --> 01:01:19.870
and because splitting based on type.

01:01:20.590 --> 01:01:22.310
I end up no matter what type of

01:01:22.310 --> 01:01:24.200
restaurant is, I end up with an equal

01:01:24.200 --> 01:01:26.120
number of greens and Reds.

01:01:26.120 --> 01:01:30.140
So green green means I didn't like say

01:01:30.140 --> 01:01:32.672
it very clearly, but green means that

01:01:32.672 --> 01:01:35.842
you think that you go, that you wait,

01:01:35.842 --> 01:01:37.540
and red means that you don't wait.

01:01:38.460 --> 01:01:40.820
So type tells me nothing, right?

01:01:40.820 --> 01:01:42.310
It doesn't help me split anything at

01:01:42.310 --> 01:01:42.455
all.

01:01:42.455 --> 01:01:44.898
I knew initially I had complete Entropy

01:01:44.898 --> 01:01:47.780
Entropy of 1 and after knowing type I

01:01:47.780 --> 01:01:48.880
still have Entropy of 1.

01:01:49.900 --> 01:01:52.140
Where if I know Patrons, then a lot of

01:01:52.140 --> 01:01:55.720
the time I have my Decision, and only

01:01:55.720 --> 01:01:57.230
some fraction of the time I still have

01:01:57.230 --> 01:01:57.590
to.

01:01:57.590 --> 01:01:59.040
I need more information.

01:02:00.990 --> 01:02:02.700
So here's like all the math.

01:02:04.250 --> 01:02:05.230
To go through that but.

01:02:08.910 --> 01:02:11.790
All right, So what if I?

01:02:12.780 --> 01:02:14.730
So sometimes a lot of times trees are

01:02:14.730 --> 01:02:16.930
used for continuous values and then

01:02:16.930 --> 01:02:18.320
it's called a Regression tree.

01:02:20.760 --> 01:02:22.960
The Regression tree is learned in the

01:02:22.960 --> 01:02:23.510
same way.

01:02:24.570 --> 01:02:29.490
Except that you would use the instead

01:02:29.490 --> 01:02:30.840
of, sorry.

01:02:32.260 --> 01:02:34.170
In the Regression tree, it's the same

01:02:34.170 --> 01:02:36.530
way, but you're typically trying to

01:02:36.530 --> 01:02:38.703
minimize the sum of squared error of

01:02:38.703 --> 01:02:41.862
the node instead of minimizing the

01:02:41.862 --> 01:02:42.427
cross entropy.

01:02:42.427 --> 01:02:44.050
You could still do it actually based on

01:02:44.050 --> 01:02:45.500
cross entropy if you're seeing like

01:02:45.500 --> 01:02:47.770
Gaussian distributions, but here let me

01:02:47.770 --> 01:02:48.900
show you an example.

01:02:54.540 --> 01:02:55.230
So.

01:02:57.600 --> 01:02:59.170
Let's just say I'm doing like one

01:02:59.170 --> 01:03:00.700
feature, let's say like.

01:03:01.480 --> 01:03:04.610
This is my feature X and my prediction

01:03:04.610 --> 01:03:05.240
value.

01:03:06.000 --> 01:03:07.830
Is the number that I'm putting here.

01:03:18.340 --> 01:03:18.690
OK.

01:03:19.430 --> 01:03:20.160
So.

01:03:21.350 --> 01:03:22.980
I'm trying to predict what this number

01:03:22.980 --> 01:03:25.460
is given like where I fell on this X

01:03:25.460 --> 01:03:25.950
axis.

01:03:27.030 --> 01:03:28.940
So the best split I could do is

01:03:28.940 --> 01:03:30.550
probably like here, right?

01:03:31.330 --> 01:03:33.800
And if I take this split, then I would

01:03:33.800 --> 01:03:37.313
say that if I'm in this side of the

01:03:37.313 --> 01:03:37.879
split.

01:03:38.640 --> 01:03:42.450
Then my prediction is 4 out of three,

01:03:42.450 --> 01:03:44.560
which is the average of the values that

01:03:44.560 --> 01:03:45.690
are on this side of the split.

01:03:46.510 --> 01:03:48.710
And if I'm on this side of the split,

01:03:48.710 --> 01:03:51.030
then my prediction is 6.

01:03:51.800 --> 01:03:53.900
Which is 18 / 3, right?

01:03:53.900 --> 01:03:55.815
So it's the average of these values.

01:03:55.815 --> 01:03:58.270
So if I'm doing Regression, I'm still

01:03:58.270 --> 01:04:00.520
like I'm choosing a split that's going

01:04:00.520 --> 01:04:03.580
to give me the best prediction in each

01:04:03.580 --> 01:04:04.390
side of the split.

01:04:04.980 --> 01:04:06.745
And then my estimate on each side of

01:04:06.745 --> 01:04:08.170
the split is just the average of the

01:04:08.170 --> 01:04:10.100
values after that split.

01:04:11.000 --> 01:04:13.950
And the scoring, the scoring that I can

01:04:13.950 --> 01:04:16.120
use is the squared error.

01:04:16.120 --> 01:04:20.464
So if the squared error would be 1 -, 4

01:04:20.464 --> 01:04:22.536
thirds squared, plus 2 -, 4 thirds

01:04:22.536 --> 01:04:24.905
squared plus 1 -, 4 thirds squared plus

01:04:24.905 --> 01:04:29.049
5 -, 6 ^2 + 8 -, 6 ^2 + 5 -, 6 ^2.

01:04:29.890 --> 01:04:31.665
And so I could try like every

01:04:31.665 --> 01:04:33.549
threshold, compute my squared error

01:04:33.550 --> 01:04:35.635
given every threshold and then choose

01:04:35.635 --> 01:04:37.060
the one that gives me the lowest

01:04:37.060 --> 01:04:37.740
squared error.

01:04:41.040 --> 01:04:43.055
So it's the same algorithm, except that

01:04:43.055 --> 01:04:44.245
you have a different Criterion.

01:04:44.245 --> 01:04:46.370
You might use squared error.

01:04:47.820 --> 01:04:49.530
Because it's continuous values that I'm

01:04:49.530 --> 01:04:50.100
predicting.

01:04:50.840 --> 01:04:53.030
And then the output of the node will be

01:04:53.030 --> 01:04:54.390
the average of the Samples that fall

01:04:54.390 --> 01:04:55.069
into that node.

01:04:56.480 --> 01:04:58.300
And for Regression trees, that's

01:04:58.300 --> 01:05:00.020
especially important to.

01:05:01.330 --> 01:05:03.490
Stop growing your tree early, because

01:05:03.490 --> 01:05:05.420
obviously otherwise you're going to

01:05:05.420 --> 01:05:10.090
always separate your data into one leaf

01:05:10.090 --> 01:05:12.030
node per data point, since you have

01:05:12.030 --> 01:05:13.995
like continuous values, unless there's

01:05:13.995 --> 01:05:15.410
like many of the same value.

01:05:16.020 --> 01:05:17.410
And so you're going to tend to like

01:05:17.410 --> 01:05:17.870
overfit.

01:05:23.330 --> 01:05:25.920
Overfitting, by the way, that's a term

01:05:25.920 --> 01:05:27.060
that comes up a lot in machine

01:05:27.060 --> 01:05:27.865
learning.

01:05:27.865 --> 01:05:30.870
Overfitting means that your model you

01:05:30.870 --> 01:05:32.910
have a very complex model so that you

01:05:32.910 --> 01:05:34.940
achieve like really low Training Error.

01:05:35.660 --> 01:05:37.550
But due to the complexity you're Test

01:05:37.550 --> 01:05:38.740
error has gone up.

01:05:38.740 --> 01:05:41.570
So if you plot your.

01:05:42.250 --> 01:05:44.210
If you plot your Test error as, you

01:05:44.210 --> 01:05:45.510
increase complexity.

01:05:46.200 --> 01:05:48.000
You're Test error will go down for some

01:05:48.000 --> 01:05:50.030
time, but then at some point as your

01:05:50.030 --> 01:05:51.880
complexity keeps rising, you're Test

01:05:51.880 --> 01:05:53.590
Error will start to increase.

01:05:53.590 --> 01:05:55.040
So the point at which you're.

01:05:55.740 --> 01:05:57.650
You're Test Error increases due to

01:05:57.650 --> 01:05:59.260
increasing complexity is where you

01:05:59.260 --> 01:06:00.040
start overfitting.

01:06:00.870 --> 01:06:02.300
We'll talk about that more at the start

01:06:02.300 --> 01:06:03.000
of the ensembles.

01:06:04.840 --> 01:06:06.610
Right, so there's a few variants.

01:06:06.610 --> 01:06:08.620
You can use different splitting

01:06:08.620 --> 01:06:09.490
criteria.

01:06:09.490 --> 01:06:12.010
For example, the genie like impurity or

01:06:12.010 --> 01:06:14.580
Genie Diversity index is just one minus

01:06:14.580 --> 01:06:17.460
the sum over all the values of X

01:06:17.460 --> 01:06:18.700
probability of X ^2.

01:06:19.480 --> 01:06:22.140
This actually is like almost the same

01:06:22.140 --> 01:06:25.800
thing as the Entropy.

01:06:26.410 --> 01:06:27.800
But it's a little bit faster to

01:06:27.800 --> 01:06:29.840
compute, so it's actually more often

01:06:29.840 --> 01:06:30.740
used as the default.

01:06:33.830 --> 01:06:35.890
Most times you split on one attribute

01:06:35.890 --> 01:06:38.460
at a time, but you can also.

01:06:39.190 --> 01:06:40.820
They're in some algorithms.

01:06:40.820 --> 01:06:42.790
You can solve for slices through the

01:06:42.790 --> 01:06:44.600
feature space you can.

01:06:45.280 --> 01:06:47.490
Do like linear discriminant analysis or

01:06:47.490 --> 01:06:49.200
something like that to try to find like

01:06:49.200 --> 01:06:51.970
a multivariable split that separates

01:06:51.970 --> 01:06:53.870
the data, but usually it's just single

01:06:53.870 --> 01:06:54.310
attribute.

01:06:56.180 --> 01:06:57.970
And as I mentioned a couple of times,

01:06:57.970 --> 01:07:00.010
you can stop early so you don't need to

01:07:00.010 --> 01:07:02.010
grow like the full tree until you get

01:07:02.010 --> 01:07:03.025
perfect Training accuracy.

01:07:03.025 --> 01:07:06.110
You can stop after you reach a Max

01:07:06.110 --> 01:07:09.475
depth or stop after you have a certain

01:07:09.475 --> 01:07:11.540
number of nodes per certain number of

01:07:11.540 --> 01:07:12.620
data points per node.

01:07:13.710 --> 01:07:15.470
And the reason that you had stopped

01:07:15.470 --> 01:07:16.920
early is because you the tree to

01:07:16.920 --> 01:07:18.990
generalized new data and if you grow

01:07:18.990 --> 01:07:20.450
like a really big tree, you're going to

01:07:20.450 --> 01:07:23.000
end up with these like little like

01:07:23.000 --> 01:07:26.240
micro applicable rules that might not

01:07:26.240 --> 01:07:27.750
work well when you get new Test

01:07:27.750 --> 01:07:28.270
Samples.

01:07:29.220 --> 01:07:31.190
Where if you have a shorter tree that

01:07:31.190 --> 01:07:34.260
then you might have some uncertainty

01:07:34.260 --> 01:07:36.147
left in your leaf nodes, but you can

01:07:36.147 --> 01:07:38.300
have more confidence that will reflect

01:07:38.300 --> 01:07:39.240
the true distribution.

01:07:42.350 --> 01:07:45.630
So if we look at Decision trees versus

01:07:45.630 --> 01:07:46.280
one and north.

01:07:46.980 --> 01:07:49.500
They're actually kind of similar in a

01:07:49.500 --> 01:07:49.950
way.

01:07:49.950 --> 01:07:51.620
They both have piecewise linear

01:07:51.620 --> 01:07:52.120
decisions.

01:07:52.750 --> 01:07:54.620
So here's the boundary that I get with

01:07:54.620 --> 01:07:56.420
one and N in this example.

01:07:57.110 --> 01:08:00.550
It's going to be based on like if you

01:08:00.550 --> 01:08:03.380
chop things up into cells where each

01:08:03.380 --> 01:08:05.770
sample is like everything within the

01:08:05.770 --> 01:08:07.550
cell is closest to a particular sample.

01:08:08.260 --> 01:08:09.460
I would get this boundary.

01:08:11.100 --> 01:08:12.915
And with the Decision tree you tend to

01:08:12.915 --> 01:08:14.440
get, if you're doing 1 attribute at a

01:08:14.440 --> 01:08:15.980
time, you get this access to line

01:08:15.980 --> 01:08:16.630
boundary.

01:08:16.630 --> 01:08:18.832
So it ends up being like going straight

01:08:18.832 --> 01:08:20.453
over and then up and then straight over

01:08:20.453 --> 01:08:22.160
and then down and then a little bit

01:08:22.160 --> 01:08:23.320
over and then down.

01:08:23.320 --> 01:08:25.226
But they're kind of similar.

01:08:25.226 --> 01:08:28.220
So they're the overlap of those spaces

01:08:28.220 --> 01:08:28.690
is similar.

01:08:31.900 --> 01:08:34.170
The Decision tree also has the ability

01:08:34.170 --> 01:08:36.042
for over stopping to improve

01:08:36.042 --> 01:08:36.520
generalization.

01:08:36.520 --> 01:08:38.530
While they can and doesn't the K&N you

01:08:38.530 --> 01:08:40.700
can increase K to try to improve

01:08:40.700 --> 01:08:42.110
generalization to make it like a

01:08:42.110 --> 01:08:44.506
smoother boundary, but it doesn't have

01:08:44.506 --> 01:08:46.540
like as doesn't have very many like

01:08:46.540 --> 01:08:47.930
controls or knobs to tune.

01:08:50.390 --> 01:08:53.010
And the true power that Decision trees

01:08:53.010 --> 01:08:54.580
arise with ensembles.

01:08:54.580 --> 01:08:56.920
So if you combine lots of these trees

01:08:56.920 --> 01:08:59.250
together to make a prediction, then

01:08:59.250 --> 01:09:01.050
suddenly it becomes very effective.

01:09:01.750 --> 01:09:04.430
In practice, people don't usually use

01:09:04.430 --> 01:09:06.620
this one Decision tree in machine

01:09:06.620 --> 01:09:07.998
learning to make an automated

01:09:07.998 --> 01:09:08.396
prediction.

01:09:08.396 --> 01:09:10.710
They usually use a whole bunch of them

01:09:10.710 --> 01:09:12.397
and then average the results or train

01:09:12.397 --> 01:09:14.870
them in a way that they that they

01:09:14.870 --> 01:09:17.126
incrementally build up your prediction.

01:09:17.126 --> 01:09:18.850
And that's what I'll talk about when I

01:09:18.850 --> 01:09:19.730
talk about ensembles.

01:09:22.360 --> 01:09:23.750
So Decision trees are really a

01:09:23.750 --> 01:09:26.740
component in two of the most successful

01:09:26.740 --> 01:09:28.970
algorithms of all time, but they're not

01:09:28.970 --> 01:09:29.630
the whole thing.

01:09:30.940 --> 01:09:33.160
Here's an example of a Regression tree

01:09:33.160 --> 01:09:34.470
for Temperature prediction.

01:09:35.560 --> 01:09:37.200
Just so that I can make the tree simple

01:09:37.200 --> 01:09:39.370
enough to put on a Slide, I set the Min

01:09:39.370 --> 01:09:41.840
leaf size to 200 so there.

01:09:41.840 --> 01:09:44.000
So I stopped splitting once the node

01:09:44.000 --> 01:09:44.990
has 200 points.

01:09:46.120 --> 01:09:49.080
And then I computed the root mean

01:09:49.080 --> 01:09:50.450
squared error and the R2.

01:09:51.680 --> 01:09:53.280
And so you can see for example like.

01:09:54.430 --> 01:09:55.990
One thing that is interesting to me

01:09:55.990 --> 01:09:58.278
about this is that I would have thought

01:09:58.278 --> 01:09:59.872
that the temperature in Cleveland

01:09:59.872 --> 01:10:01.510
yesterday would be the best predictor

01:10:01.510 --> 01:10:03.150
of the temperature in Cleveland today,

01:10:03.150 --> 01:10:05.056
but it's actually not the best

01:10:05.056 --> 01:10:05.469
predictor.

01:10:05.470 --> 01:10:09.090
So the best single like criteria is the

01:10:09.090 --> 01:10:11.090
temperature in Chicago yesterday,

01:10:11.090 --> 01:10:13.590
because I guess the weather like moves

01:10:13.590 --> 01:10:15.460
from West to east a bit.

01:10:16.850 --> 01:10:19.665
And I guess downward, so knowing the

01:10:19.665 --> 01:10:21.477
weather in Chicago yesterday, whether

01:10:21.477 --> 01:10:23.420
the weather was less than whether the

01:10:23.420 --> 01:10:25.530
Temperature was less than 8.4 Celsius

01:10:25.530 --> 01:10:26.950
or greater than 8.4 Celsius.

01:10:27.590 --> 01:10:29.040
Is the best single thing that I can

01:10:29.040 --> 01:10:29.290
know.

01:10:30.480 --> 01:10:31.160
And then?

01:10:32.290 --> 01:10:34.920
That reduces my initial squared error

01:10:34.920 --> 01:10:36.400
was 112.

01:10:38.170 --> 01:10:39.680
And then if you divide it by number of

01:10:39.680 --> 01:10:41.560
Samples, then or.

01:10:42.810 --> 01:10:44.720
Yeah, take divided by number of samples

01:10:44.720 --> 01:10:45.960
and take square root or something to

01:10:45.960 --> 01:10:47.390
get the per sample.

01:10:48.300 --> 01:10:51.010
Then depending on that answer, then I

01:10:51.010 --> 01:10:53.209
check to see what is the temperature in

01:10:53.210 --> 01:10:55.458
Milwaukee yesterday or what is the

01:10:55.458 --> 01:10:57.140
temperature in Grand Rapids yesterday.

01:10:58.060 --> 01:10:59.600
And then depending on those answers, I

01:10:59.600 --> 01:11:02.040
check Chicago again, a different value

01:11:02.040 --> 01:11:04.170
of Chicago, and then I get my final

01:11:04.170 --> 01:11:04.840
decision here.

01:11:11.120 --> 01:11:13.720
Yeah, it's like my sister lives in

01:11:13.720 --> 01:11:16.140
Harrisburg, so I always know that

01:11:16.140 --> 01:11:17.750
they're going to get our weather like a

01:11:17.750 --> 01:11:18.240
day later.

01:11:19.020 --> 01:11:20.680
So it's like, it's really warm here.

01:11:20.680 --> 01:11:22.190
They're like, it's cold, it's warm

01:11:22.190 --> 01:11:22.450
here.

01:11:22.450 --> 01:11:23.600
Well, I guess it will be warm for you

01:11:23.600 --> 01:11:24.930
tomorrow or in two days.

01:11:26.130 --> 01:11:26.620
Yeah.

01:11:27.540 --> 01:11:29.772
But part of the reason that I share

01:11:29.772 --> 01:11:31.300
this is that the one thing that's

01:11:31.300 --> 01:11:32.890
really cool about Decision trees is

01:11:32.890 --> 01:11:34.910
that you get some explanation, like you

01:11:34.910 --> 01:11:37.450
can understand the data better by

01:11:37.450 --> 01:11:39.600
looking at the tree like this kind of

01:11:39.600 --> 01:11:41.860
violated my initial assumption that the

01:11:41.860 --> 01:11:43.340
best thing to know for the Temperature

01:11:43.340 --> 01:11:44.830
is your Temperature the previous day.

01:11:45.460 --> 01:11:46.600
It's actually the temperature of

01:11:46.600 --> 01:11:48.965
another city the previous day and you

01:11:48.965 --> 01:11:51.100
can get you can create these rules that

01:11:51.100 --> 01:11:53.030
help you understand, like how to make

01:11:53.030 --> 01:11:53.740
predictions.

01:11:56.130 --> 01:11:56.710
This is.

01:11:56.710 --> 01:11:58.320
I'm not expecting you to read this now,

01:11:58.320 --> 01:12:00.370
but this is the code to generate this

01:12:00.370 --> 01:12:00.820
tree.

01:12:06.080 --> 01:12:07.600
Right on Summary.

01:12:08.580 --> 01:12:10.800
The key assumptions of this of the

01:12:10.800 --> 01:12:12.570
Classification or Regression trees are

01:12:12.570 --> 01:12:15.255
that Samples with similar features have

01:12:15.255 --> 01:12:16.070
similar predictions.

01:12:16.070 --> 01:12:17.590
So it's a similar assumption in Nearest

01:12:17.590 --> 01:12:19.580
neighbor, except this time we're trying

01:12:19.580 --> 01:12:21.680
to figure out how to like split up the

01:12:21.680 --> 01:12:23.420
feature space to define that

01:12:23.420 --> 01:12:25.159
similarity, rather than using like a

01:12:25.160 --> 01:12:29.090
preset distance function like Euclidean

01:12:29.090 --> 01:12:29.560
distance.

01:12:30.970 --> 01:12:32.610
The model parameters are the split

01:12:32.610 --> 01:12:34.560
criteria, each internal node, and then

01:12:34.560 --> 01:12:36.630
the final prediction at each leaf node.

01:12:38.200 --> 01:12:40.020
The designs are putting limits on the

01:12:40.020 --> 01:12:42.080
tree growth and what kinds of splits

01:12:42.080 --> 01:12:43.545
you can consider, like whether to split

01:12:43.545 --> 01:12:45.260
on one attribute or whole groups of

01:12:45.260 --> 01:12:48.930
attributes and then choosing their

01:12:48.930 --> 01:12:50.030
criteria for this split.

01:12:51.520 --> 01:12:52.120


01:12:53.300 --> 01:12:56.060
You Decision trees by themselves are

01:12:56.060 --> 01:12:57.645
useful if you want some explainable

01:12:57.645 --> 01:12:58.710
Decision function.

01:12:58.710 --> 01:13:00.270
So they could be used for like medical

01:13:00.270 --> 01:13:02.090
diagnosis for example, because you want

01:13:02.090 --> 01:13:03.750
to be able to tell people like why.

01:13:04.710 --> 01:13:07.324
Like why I know you have cancer, like

01:13:07.324 --> 01:13:08.840
you don't want to just be like I use

01:13:08.840 --> 01:13:10.270
this machine learning algorithm and it

01:13:10.270 --> 01:13:12.070
says you have like a 93% chance of

01:13:12.070 --> 01:13:13.750
having cancer and so sorry.

01:13:15.000 --> 01:13:16.785
You want to be able to say like because

01:13:16.785 --> 01:13:19.086
of like this thing and because of this

01:13:19.086 --> 01:13:21.099
thing and because of this thing like

01:13:21.100 --> 01:13:24.919
out of all these 1500 cases like 90% of

01:13:24.920 --> 01:13:26.750
them ended up having cancer.

01:13:26.750 --> 01:13:28.180
So we need to do, we need to do a

01:13:28.180 --> 01:13:29.110
biopsy, right.

01:13:29.110 --> 01:13:30.305
So you want some explanation.

01:13:30.305 --> 01:13:31.900
A lot of times it's not always good

01:13:31.900 --> 01:13:33.600
enough to have like a good prediction.

01:13:35.590 --> 01:13:37.240
And they're also like really effective

01:13:37.240 --> 01:13:38.520
as part of a ensemble.

01:13:38.520 --> 01:13:39.650
And again, I think we might see a

01:13:39.650 --> 01:13:40.650
Tuesday instead of Thursday.

01:13:43.150 --> 01:13:44.960
It's not like a really good predictor

01:13:44.960 --> 01:13:47.320
by itself, but it is really good as

01:13:47.320 --> 01:13:47.770
part of an.

01:13:48.500 --> 01:13:48.790
Alright.

01:13:49.670 --> 01:13:51.250
So things you remember, Decision

01:13:51.250 --> 01:13:52.690
Regression trees learn to split up the

01:13:52.690 --> 01:13:54.590
feature space into partitions into

01:13:54.590 --> 01:13:56.110
different cells with similar values.

01:13:57.150 --> 01:13:59.070
And then Entropy is a really important

01:13:59.070 --> 01:13:59.600
concept.

01:13:59.600 --> 01:14:01.030
It's a measure of uncertainty.

01:14:02.730 --> 01:14:05.170
Information gain measures how much

01:14:05.170 --> 01:14:07.090
particular knowledge reduces the

01:14:07.090 --> 01:14:08.710
prediction uncertainty, and that's the

01:14:08.710 --> 01:14:10.260
basis for forming our tree.

01:14:11.630 --> 01:14:13.650
So on Thursday I'm going to do a bit of

01:14:13.650 --> 01:14:15.680
review of our concepts and then I think

01:14:15.680 --> 01:14:17.200
most likely next Tuesday I'll talk

01:14:17.200 --> 01:14:19.730
about ensembles and random forests and

01:14:19.730 --> 01:14:21.540
give you an extensive example of how

01:14:21.540 --> 01:14:23.560
it's used in the Kinect algorithm.

01:14:24.800 --> 01:14:25.770
Alright, thanks everyone.

01:14:25.770 --> 01:14:26.660
See you Thursday.

01:19:07.020 --> 01:19:08.790
Hello.

01:19:10.510 --> 01:19:11.430
Training an assault.