Sum-of-Squares Polynomial Flow

Priyank Jaini, Kira A. Selby, Yaoliang Yu
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:3009-3018, 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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-jaini19a, title = {Sum-of-Squares Polynomial Flow}, author = {Jaini, Priyank and Selby, Kira A. and Yu, Yaoliang}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {3009--3018}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/jaini19a/jaini19a.pdf}, url = {https://proceedings.mlr.press/v97/jaini19a.html}, 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 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.} }
Endnote
%0 Conference Paper %T Sum-of-Squares Polynomial Flow %A Priyank Jaini %A Kira A. Selby %A Yaoliang Yu %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-jaini19a %I PMLR %P 3009--3018 %U https://proceedings.mlr.press/v97/jaini19a.html %V 97 %X 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.
APA
Jaini, P., Selby, K.A. & Yu, Y.. (2019). Sum-of-Squares Polynomial Flow. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:3009-3018 Available from https://proceedings.mlr.press/v97/jaini19a.html.

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