Timezone: »
We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability distributions not directly amenable to the reparameterization trick: Gamma, Beta, and Dirichlet. We further observe that when the reparameterization trick is applied to the Cholesky-factorized multivariate Normal distribution, the resulting gradients are suboptimal in the sense of optimal transport. We derive the optimal gradients and show that they have reduced variance in a Gaussian Process regression task. We demonstrate with a variety of synthetic experiments and stochastic variational inference tasks that our pathwise gradients are competitive with other methods.
Author Information
Martin Jankowiak (Uber AI Labs)
Fritz Obermeyer (Uber AI Labs)
Related Events (a corresponding poster, oral, or spotlight)
-
2018 Oral: Pathwise Derivatives Beyond the Reparameterization Trick »
Fri Jul 13th 03:50 -- 04:00 PM Room A4
More from the Same Authors
-
2019 : Poster Session 1 (all papers) »
Matilde Gargiani · Yochai Zur · Chaim Baskin · Evgenii Zheltonozhskii · Liam Li · Ameet Talwalkar · Xuedong Shang · HARKIRAT Behl · Atilim Gunes Baydin · Ivo Couckuyt · Tom Dhaene · Chieh Hubert Lin · Wei Wei · Min Sun · Orchid Majumder · Michele Donini · Yoshihiko Ozaki · Ryan P. Adams · Christian Geißler · Ping Luo · zhanglin peng · shaowenqi · Ruimao Zhang · John Langford · Rich Caruana · Debadeepta Dey · Charles Weill · Xavi Gonzalvo · Scott Yang · Scott Yak · Eugen Hotaj · vlejd Macko · Mehryar Mohri · Corinna Cortes · Stefan Webb · JP Chen · Martin Jankowiak · Noah Goodman · Aaron Klein · Frank Hutter · Mojan Javaheripi · Mohammad Samragh · Sungbin Lim · Taesup Kim · SUNGWOONG KIM · Michael Volpp · Iddo Drori · Yamuna Krishnamurthy · Kyunghyun Cho · Stanislaw Jastrzebski · Quentin de Laroussilhe · Mingxing Tan · Xiao Ma · Neil Houlsby · Andrea Gesmundo · Zalán Borsos · Krzysztof Maziarz · Felipe Petroski Such · Joel Lehman · Ken Stanley · Jeff Clune · Pieter Gijsbers · Joaquin Vanschoren · Felix Mohr · Eyke Hüllermeier · Zheng Xiong · Wenpeng Zhang · wenwu zhu · Weijia Shao · Aleksandra Faust · Michal Valko · Michael Y Li · hugojair Escalante · Marcel Wever · Andrey Khorlin · Tara Javidi · Anthony Francis · Saurajit Mukherjee · Jungtaek Kim · Michael McCourt · Saehoon Kim · Tackgeun You · Seungjin Choi · Nicolas Knudde · Alexander Tornede · Ghassen Jerfel -
2019 Poster: Tensor Variable Elimination for Plated Factor Graphs »
Fritz Obermeyer · Eli Bingham · Martin Jankowiak · Neeraj Pradhan · Justin Chiu · Alexander Rush · Noah Goodman -
2019 Oral: Tensor Variable Elimination for Plated Factor Graphs »
Fritz Obermeyer · Eli Bingham · Martin Jankowiak · Neeraj Pradhan · Justin Chiu · Alexander Rush · Noah Goodman