Sum-of-Squares Polynomial Flow
Priyank Jaini · Kira A. Selby · Yaoliang Yu

Wed Jun 12th 11:00 -- 11:20 AM @ Hall A

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 high-dimensional density estimation, by specifying one-dimensional 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 Sum-of-Squares (SOS) flow that is interpretable, universal, and easy to train. We perform several synthetic experiments on various density geometries to demonstrate the benefits (and short-comings) of such transformations. SOS flows achieve competitive results in simulations and several real-world datasets.

Author Information

Priyank Jaini (University of Waterloo, Vector Institute)
Kira A. Selby (University of Waterloo)
Yaoliang Yu (University of Waterloo)

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