Timezone: »
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably hard. We consider the case of stronger structural assumptions that are commonly satisfied in modern machine learning, including representation learning and generative modelling with autoencoder architectures. Under these assumptions we propose and study an estimator that can be easily implemented, works well in high dimensions, and enjoys faster rates of convergence. We verify the behavior of our estimator empirically in both synthetic and real-data experiments, and discuss its direct implications for total correlation, entropy, and mutual information estimation.
Author Information
Paul Rubenstein (MPI for IS)
Olivier Bousquet (Google Brain (Zurich))
Josip Djolonga (Google Research, Brain Team)
Carlos Riquelme (Google Brain)
Ilya Tolstikhin (MPI for Intelligent Systems)
More from the Same Authors
-
2021 : Uncertainty Baselines: Benchmarks for Uncertainty & Robustness in Deep Learning »
Zachary Nado · Neil Band · Mark Collier · Josip Djolonga · Mike Dusenberry · Sebastian Farquhar · Qixuan Feng · Angelos Filos · Marton Havasi · Rodolphe Jenatton · Ghassen Jerfel · Jeremiah Liu · Zelda Mariet · Jeremy Nixon · Shreyas Padhy · Jie Ren · Tim G. J. Rudner · Yeming Wen · Florian Wenzel · Kevin Murphy · D. Sculley · Balaji Lakshminarayanan · Jasper Snoek · Yarin Gal · Dustin Tran -
2022 Poster: On the Adversarial Robustness of Mixture of Experts »
Joan Puigcerver · Rodolphe Jenatton · Carlos Riquelme · Pranjal Awasthi · Srinadh Bhojanapalli -
2022 Poster: Multimodal Contrastive Learning with LIMoE: the Language-Image Mixture of Experts »
Basil Mustafa · Carlos Riquelme · Joan Puigcerver · Rodolphe Jenatton · Neil Houlsby -
2021 Poster: MLP-Mixer: An all-MLP Architecture for Vision »
Ilya Tolstikhin · Neil Houlsby · Alexander Kolesnikov · Lucas Beyer · Xiaohua Zhai · Thomas Unterthiner · Jessica Yung · Andreas Steiner · Daniel Keysers · Jakob Uszkoreit · Mario Lucic · Alexey Dosovitskiy -
2021 Poster: Scaling Vision with Sparse Mixture of Experts »
Carlos Riquelme · Joan Puigcerver · Basil Mustafa · Maxim Neumann · Rodolphe Jenatton · André Susano Pinto · Daniel Keysers · Neil Houlsby -
2021 Poster: Revisiting the Calibration of Modern Neural Networks »
Matthias Minderer · Josip Djolonga · Rob Romijnders · Frances Hubis · Xiaohua Zhai · Neil Houlsby · Dustin Tran · Mario Lucic -
2020 Memorial: In Memory of Olivier Chapelle »
Bernhard Schölkopf · Andre Elisseeff · Olivier Bousquet · Vladimir Vapnik · Jason E Weston -
2020 Poster: Synthetic Data Generators -- Sequential and Private »
Olivier Bousquet · Roi Livni · Shay Moran -
2020 Poster: What Do Neural Networks Learn When Trained With Random Labels? »
Hartmut Maennel · Ibrahim Alabdulmohsin · Ilya Tolstikhin · Robert Baldock · Olivier Bousquet · Sylvain Gelly · Daniel Keysers -
2020 Spotlight: What Do Neural Networks Learn When Trained With Random Labels? »
Hartmut Maennel · Ibrahim Alabdulmohsin · Ilya Tolstikhin · Robert Baldock · Olivier Bousquet · Sylvain Gelly · Daniel Keysers -
2019 : Poster Session »
Gergely Flamich · Shashanka Ubaru · Charles Zheng · Josip Djolonga · Kristoffer Wickstrøm · Diego Granziol · Konstantinos Pitas · Jun Li · Robert Williamson · Sangwoong Yoon · Kwot Sin Lee · Julian Zilly · Linda Petrini · Ian Fischer · Zhe Dong · Alexander Alemi · Bao-Ngoc Nguyen · Rob Brekelmans · Tailin Wu · Aditya Mahajan · Alexander Li · Kirankumar Shiragur · Yair Carmon · Linara Adilova · SHIYU LIU · Bang An · Sanjeeb Dash · Oktay Gunluk · Arya Mazumdar · Mehul Motani · Julia Rosenzweig · Michael Kamp · Marton Havasi · Leighton P Barnes · Zhengqing Zhou · Yi Hao · Dylan Foster · Yuval Benjamini · Nati Srebro · Michael Tschannen · Paul Rubenstein · Sylvain Gelly · John Duchi · Aaron Sidford · Robin Ru · Stefan Zohren · Murtaza Dalal · Michael A Osborne · Stephen J Roberts · Moses Charikar · Jayakumar Subramanian · Xiaodi Fan · Max Schwarzer · Nicholas Roberts · Simon Lacoste-Julien · Vinay Prabhu · Aram Galstyan · Greg Ver Steeg · Lalitha Sankar · Yung-Kyun Noh · Gautam Dasarathy · Frank Park · Ngai-Man (Man) Cheung · Ngoc-Trung Tran · Linxiao Yang · Ben Poole · Andrea Censi · Tristan Sylvain · R Devon Hjelm · Bangjie Liu · Jose Gallego-Posada · Tyler Sypherd · Kai Yang · Jan Nikolas Morshuis -
2019 Poster: Adaptive Temporal-Difference Learning for Policy Evaluation with Per-State Uncertainty Estimates »
Carlos Riquelme · Hugo Penedones · Damien Vincent · Hartmut Maennel · Sylvain Gelly · Timothy A Mann · Andre Barreto · Gergely Neu -
2018 Poster: Provable Variational Inference for Constrained Log-Submodular Models »
Josip Djolonga · Stefanie Jegelka · Andreas Krause -
2018 Poster: Assessing Generative Models via Precision and Recall »
Mehdi S. M. Sajjadi · Olivier Bachem · Mario Lucic · Olivier Bousquet · Sylvain Gelly -
2018 Poster: Are GANs Created Equal? A Large-Scale Study »
Mario Lucic · Karol Kurach · Marcin Michalski · Sylvain Gelly · Olivier Bousquet -
2017 Workshop: Optimal Transport and Machine Learning »
Olivier Bousquet · Marco Cuturi · Gabriel Peyré · Fei Sha · Justin Solomon -
2017 : Poster Session »
Shunsuke Horii · Heejin Jeong · Tobias Schwedes · Qing He · Ben Calderhead · Ertunc Erdil · Jaan Altosaar · Patrick Muchmore · Rajiv Khanna · Ian Gemp · Pengfei Zhang · Yuan Zhou · Chris Cremer · Maria DeYoreo · Alexander Terenin · Brendan McVeigh · Rachit Singh · Yaodong Yang · Erik Bodin · Trefor Evans · Henry Chai · Shandian Zhe · Jeffrey Ling · Vincent ADAM · Lars Maaløe · Andrew Miller · Ari Pakman · Josip Djolonga · Hong Ge -
2017 : Contributed talk: Learning Implicit Generative Models Using Differentiable Graph Tests »
Josip Djolonga -
2017 Poster: Approximation and Convergence Properties of Generative Adversarial Learning »
Shuang Liu · Olivier Bousquet · Kamalika Chaudhuri -
2017 Spotlight: Approximation and Convergence Properties of Generative Adversarial Learning »
Shuang Liu · Olivier Bousquet · Kamalika Chaudhuri -
2017 Poster: Differentiable Learning of Submodular Functions »
Josip Djolonga · Andreas Krause -
2017 Spotlight: Differentiable Learning of Submodular Functions »
Josip Djolonga · Andreas Krause -
2017 Poster: AdaGAN: Boosting Generative Models »
Ilya Tolstikhin · Sylvain Gelly · Olivier Bousquet · Carl-Johann SIMON-GABRIEL · Bernhard Schölkopf -
2016 Poster: Minimax Estimation of Maximum Mean Discrepancy with Radial Kernels »
Ilya Tolstikhin · Bharath Sriperumbudur · Bernhard Schölkopf -
2016 Poster: Variational Inference in Mixed Probabilistic Submodular Models »
Josip Djolonga · Sebastian Tschiatschek · Andreas Krause -
2016 Poster: Cooperative Graphical Models »
Josip Djolonga · Stefanie Jegelka · Sebastian Tschiatschek · Andreas Krause -
2016 Poster: Consistent Kernel Mean Estimation for Functions of Random Variables »
Carl-Johann Simon-Gabriel · Adam Scibior · Ilya Tolstikhin · Bernhard Schölkopf -
2014 Poster: From MAP to Marginals: Variational Inference in Bayesian Submodular Models »
Josip Djolonga · Andreas Krause -
2013 Poster: High-Dimensional Gaussian Process Bandits »
Josip Djolonga · Andreas Krause · Volkan Cevher -
2013 Poster: PAC-Bayes-Empirical-Bernstein Inequality »
Ilya Tolstikhin · Yevgeny Seldin -
2013 Spotlight: PAC-Bayes-Empirical-Bernstein Inequality »
Ilya Tolstikhin · Yevgeny Seldin -
2007 Poster: The Tradeoffs of Large Scale Learning »
Leon Bottou · Olivier Bousquet