SumofSquares Polynomial Flow
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:30093018, 2019.
Abstract
Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for highdimensional density estimation, by specifying onedimensional transformations (equivalently conditional densities) and appropriate conditioner networks. This framework (a) reveals the commonalities and differences of existing autoregressive and flow based methods, (b) allows a unified understanding of the limitations and representation power of these recent approaches and, (c) motivates us to uncover a new SumofSquares (SOS) flow that is interpretable, universal, and easy to train. We perform several synthetic experiments on various density geometries to demonstrate the benefits (and shortcomings) of such transformations. SOS flows achieve competitive results in simulations and several realworld datasets.
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