Subtractive Mixture Models via Squaring: Representation and Learning

Published in arXiv 2023

Authors: Lorenzo Loconte, Aleksanteri M. Sladek, Stefan Mengel, Martin Trapp, Arno Solin, Nicolas Gillis, Antonio Vergari

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.

title={Subtractive Mixture Models via Squaring: Representation and Learning},
author={Lorenzo Loconte and Aleksanteri M. Sladek and Stefan Mengel and Martin Trapp and Arno Solin and Nicolas Gillis and Antonio Vergari},
journal={arXiv preprint arXiv:2310.00724},
year={2023} }