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arXiv · 2302.14202

Mixtures of All Trees

Nikil Roashan Selvam·Honghua Zhang·Guy Van den Broeck
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Abstract

Tree-shaped graphical models are widely used for their tractability. However, they unfortunately lack expressive power as they require committing to a particular sparse dependency structure. We propose a novel class of generative models called mixtures of all trees: that is, a mixture over all possible ($n^{n-2}$) tree-shaped graphical models over $n$ variables. We show that it is possible to parameterize this Mixture of All Trees (MoAT) model compactly (using a polynomial-size representation) in a way that allows for tractable likelihood computation and optimization via stochastic gradient descent. Furthermore, by leveraging the tractability of tree-shaped models, we devise fast-converging conditional sampling algorithms for approximate inference, even though our theoretical analysis suggests that exact computation of marginals in the MoAT model is NP-hard. Empirically, MoAT achieves state-of-the-art performance on density estimation benchmarks when compared against powerful probabilistic models including hidden Chow-Liu Trees.

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Nikil Roashan Selvam, Honghua Zhang, Guy Van den Broeck. 2023-02-27. Mixtures of All Trees. https://arxiv.org/abs/2302.14202

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