README.md

---
title: VendiScore
datasets:
-  
tags:
- evaluate
- metric
description: "The Vendi Score is a metric for evaluating diversity in machine learning. See the project's README at https://github.com/vertaix/Vendi-Score for more information."
sdk: gradio
sdk_version: 3.0.2
app_file: app.py
pinned: false
---

# Metric Card for VendiScore

The Vendi Score (VS) is a metric for evaluating diversity in machine learning.
The input to metric is a collection of samples and a pairwise similarity function, and the output is a number, which can be interpreted as the effective number of unique elements in the sample.
See the project's README at https://github.com/vertaix/Vendi-Score for more information.

## Metric Description
The Vendi Score (VS) is a metric for evaluating diversity in machine learning.
The input to metric is a collection of samples and a pairwise similarity function, and the output is a number, which can be interpreted as the effective number of unique elements in the sample.
Specifically, given a positive semi-definite matrix $K \in \mathbb{R}^{n \times n}$ of similarity scores, the score is defined as:
$$\mathrm{VS}(K) = \exp(-\mathrm{tr}(K/n \log K/n)) = \exp(-\sum_{i=1}^n \lambda_i \log \lambda_i),$$
where $\lambda_i$ are the eigenvalues of $K/n$ and $0 \log 0 = 0$.
That is, the Vendi Score is equal to the exponential of the von Neumann entropy of $K/n$, or the Shannon entropy of the eigenvalues, which is also known as the effective rank.

## How to Use
The Vendi Score is available as a Python package or in HuggingFace `evaluate`.
To use the Python package, see the instructions at https://github.com/vertaix/Vendi-Score.
To use the `evaluate` module, pass a list of samples and a similarity function or a string identifying a predefined class of similarity functions (see below).

```
>>> vendiscore = evaluate.load("danf0/vendiscore")
>>> samples = ["Look, Jane.",
               "See Spot.",
               "See Spot run.",
               "Run, Spot, run.",
	       "Jane sees Spot run."]
>>> results = vendiscore.compute(samples, k="ngram_overlap", ns=[1, 2])
>>> print(results)
{'VS': 3.90657...}
```

### Inputs
- **samples**: an iterable containing $n$ samples to score; an n x n similarity
       matrix K, or an n x d feature matrix X.
- **k**: a pairwise similarity function, or a string identifying a predefined 
       similarity function. If k is a pairwise similarity function, it should
       be symmetric and k(x, x) = 1.
       Options: ngram_overlap, text_embeddings, pixels, image_embeddings.
- **score_K**: if true, samples is an n x n similarity matrix K.
- **score_X**: if true, samples is an n x d feature matrix X.
- **score_dual**: if true,  samples is an n x d feature matrix X and we will
       compute the diversity score using the covariance matrix X @ X.T.
- **normalize**: if true, normalize the similarity scores.
- **model (optional)**: if k is "text_embeddings", a model mapping sentences to
       embeddings (output should be an object with an attribute called
       `pooler_output` or `last_hidden_state`). If k is "image_embeddings", a
       model mapping images to embeddings.
- **tokenizer (optional)**: if k is "text_embeddings" or "ngram_overlap", a
       tokenizer mapping strings to lists.
- **transform (optional)**: if k is "image_embeddings", a torchvision transform
       to apply to the samples.
- **model_path (optional)**: if k is "text_embeddings", the name of a model on
       the HuggingFace hub.
- **ns (optional)**: if k is "ngram_overlap", the values of n to calculate.
- **batch_size (optional)**: batch size to use if k is "text_embedding" or
       "image_embedding".
- **device (optional)**: a string (e.g. "cuda", "cpu") or torch.device 
       identifying the device to use if k is "text_embedding"
       or "image_embedding".


### Output Values

The output is a dictionary with one key, "VS".
Given n samples, the value of the Vendi Score ranges between 1 and n, with higher numbers indicating that the sample is more diverse.

### Examples

```
>>> import numpy as np
>>> vendiscore = evaluate.load("danf0/vendiscore")
>>> samples = [0, 0, 10, 10, 20, 20]
>>> k = lambda a, b: np.exp(-np.abs(a - b))
>>> vendiscore.compute(samples, k)
2.9999
```

If you already have precomputed a similarity matrix:
```
>>> K = np.array([[1.0, 0.9, 0.0],
                  [0.9, 1.0, 0.0],
                  [0.0, 0.0, 1.0]])
>>> vendiscore.compute(K, score_K=True)
2.1573
```

If your similarity function is a dot product between `n` normalized
`d`-dimensional embeddings `X`, and `d` < `n`, it is faster
to compute the Vendi Score using the covariance matrix, `X @ X.T`.
(If the rows of `X` are not normalized, set `normalize = True`.)
```
>>> X = np.array([[100, 0], [99, 1], [1, 99], [0, 100])
>>> vendiscore.compute(X, score_dual=True, normalize=True)
1.9989...
```

Image similarity can be calculated using inner products between pixel vectors or between embeddings from a neural network.
The default embeddings are from the pool-2048 layer of the torchvision version of the Inception v3 model; other embedding functions can be passed to the `model` argument.
```
>>> from torchvision import datasets
>>> mnist = datasets.MNIST("data/mnist", train=False, download=True)
>>> digits = [[x for x, y in mnist if y == c] for c in range(10)]
>>> pixel_vs = [vendiscore.compute(imgs, k="pixels") for imgs in digits]
>>> inception_vs = [vendiscore.compute(imgs, k="image_embeddings", batch_size=64, device="cuda") for imgs in digits]
>>> for y, (pvs, ivs) in enumerate(zip(pixel_vs, inception_vs)): print(f"{y}\t{pvs:.02f}\t{ivs:02f}")
0       7.68    3.45
1       5.31    3.50
2       12.18   3.62
3       9.97    2.97
4       11.10   3.75
5       13.51   3.16
6       9.06    3.63
7       9.58    4.07
8       9.69    3.74
9       8.56    3.43
```

Text similarity can be calculated using n-gram overlap or using inner products between embeddings from a neural network.
```
>>> sents = ["Look, Jane.",
             "See Spot.",
             "See Spot run.",
             "Run, Spot, run.",
	     "Jane sees Spot run."]
>>> ngram_vs = vendiscore.compute(sents, k="ngram_overlap", ns=[1, 2])
>>> bert_vs = vendiscore.compute(sents, k="text_embeddings", model_path="bert-base-uncased")
>>> simcse_vs = vendiscore.compute(sents, k="text_embeddings", model_path="princeton-nlp/unsup-simcse-bert-base-uncased")
>>> print(f"N-grams: {ngram_vs:.02f}, BERT: {bert_vs:.02f}, SimCSE: {simcse_vs:.02f})
N-grams: 3.91, BERT: 1.21, SimCSE: 2.81
```

## Limitations and Bias
The Vendi Score depends on the choice of similarity function. Care should be taken to select a similarity function that reflects the features that are relevant for defining diversity in a given application.

## Citation