Subtractive Mixture Models via Squaring: Representation and Learning

Published: 16 Jan 2024, Last Modified: 11 Feb 2024ICLR 2024 spotlightEveryoneRevisionsBibTeX
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Keywords: tractable inference, distribution estimation, probabilistic circuits, tensor networks
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TL;DR: We show how to effectively represent and learn a generic class of (deep) mixture models encoding subtractions of probability distributions, and theoretically prove they can be exponentially more expressive than addition-only mixture models.
Abstract: Mixture models are traditionally represented and learned by adding several distributions as components. Allowing mixtures to subtract probability mass or density can drastically reduce the number of components needed to model complex distributions. However, learning such subtractive mixtures while ensuring they still encode a non-negative function is challenging. We investigate how to learn and perform inference on deep subtractive mixtures by squaring them. We do this in the framework of probabilistic circuits, which enable us to represent tensorized mixtures and generalize several other subtractive models. We theoretically prove that the class of squared circuits allowing subtractions can be exponentially more expressive than traditional additive mixtures; and, we empirically show this increased expressiveness on a series of real-world distribution estimation tasks.
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Submission Number: 5955
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