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metadata
title: VendiScore
datasets:
  - null
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 an n x n positive semi-definite matrix K of similarity scores, the score is defined as:

VS(K) = exp(tr(K/n @ log(K/n))) = exp(-sum_i 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