Cousins Of The Vendi Score: A Family Of Similarity-Based Diversity Metrics For Science And Machine Learning
International Conference on Artificial Intelligence and Statistics(2023)
摘要
Measuring diversity accurately is important for many scientific fields,
including machine learning (ML), ecology, and chemistry. The Vendi Score was
introduced as a generic similarity-based diversity metric that extends the Hill
number of order q=1 by leveraging ideas from quantum statistical mechanics.
Contrary to many diversity metrics in ecology, the Vendi Score accounts for
similarity and does not require knowledge of the prevalence of the categories
in the collection to be evaluated for diversity. However, the Vendi Score
treats each item in a given collection with a level of sensitivity proportional
to the item's prevalence. This is undesirable in settings where there is a
significant imbalance in item prevalence. In this paper, we extend the other
Hill numbers using similarity to provide flexibility in allocating sensitivity
to rare or common items. This leads to a family of diversity metrics – Vendi
scores with different levels of sensitivity – that can be used in a variety of
applications. We study the properties of the scores in a synthetic controlled
setting where the ground truth diversity is known. We then test their utility
in improving molecular simulations via Vendi Sampling. Finally, we use the
Vendi scores to better understand the behavior of image generative models in
terms of memorization, duplication, diversity, and sample quality.
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