2019/05/07 by Priyank Jaini, Jaini, Priyank, Kira A. Selby +3 · 6 citations
Biochemistry, Genetics and Molecular Biology · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Metabolomics and Mass Spectrometry Studies
paper · pdf · doi:10.48550/arxiv.1905.02325
openalex publication_date 2019/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.