Timezone: »
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two-sample tests is available at github.com/fengliu90/DK-for-TST.
Author Information
Feng Liu (UTS/UCL)
Wenkai Xu (Gatsby Unit，UCL)
Jie Lu (University of Technology Sydney)
Guangquan Zhang (University of Technology Sydney)
Arthur Gretton (Gatsby Computational Neuroscience Unit)
D.J. Sutherland (TTI-Chicago)
More from the Same Authors
-
2022 : Adapting to Shifts in Latent Confounders via Observed Concepts and Proxies »
Matt Kusner · Ibrahim Alabdulmohsin · Stephen Pfohl · Olawale Salaudeen · Arthur Gretton · Sanmi Koyejo · Jessica Schrouff · Alexander D'Amour -
2023 : Prediction under Latent Subgroup Shifts with High-dimensional Observations »
William Walker · Arthur Gretton · Maneesh Sahani -
2023 Poster: A Kernel Stein Test of Goodness of Fit for Sequential Models »
Jerome Baum · Heishiro Kanagawa · Arthur Gretton -
2022 Poster: Importance Weighted Kernel Bayes' Rule »
Liyuan Xu · Yutian Chen · Arnaud Doucet · Arthur Gretton -
2022 Spotlight: Importance Weighted Kernel Bayes' Rule »
Liyuan Xu · Yutian Chen · Arnaud Doucet · Arthur Gretton -
2021 Poster: Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction »
Afsaneh Mastouri · Yuchen Zhu · Limor Gultchin · Anna Korba · Ricardo Silva · Matt J. Kusner · Arthur Gretton · Krikamol Muandet -
2021 Poster: Interpretable Stein Goodness-of-fit Tests on Riemannian Manifold »
Wenkai Xu · Takeru Matsuda -
2021 Spotlight: Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction »
Afsaneh Mastouri · Yuchen Zhu · Limor Gultchin · Anna Korba · Ricardo Silva · Matt J. Kusner · Arthur Gretton · Krikamol Muandet -
2021 Spotlight: Interpretable Stein Goodness-of-fit Tests on Riemannian Manifold »
Wenkai Xu · Takeru Matsuda -
2021 Poster: Learning Bounds for Open-Set Learning »
Zhen Fang · Jie Lu · Anjin Liu · Feng Liu · Guangquan Zhang -
2021 Spotlight: Learning Bounds for Open-Set Learning »
Zhen Fang · Jie Lu · Anjin Liu · Feng Liu · Guangquan Zhang -
2020 Poster: Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data »
Tamara Fernandez · Arthur Gretton · Nicolas Rivera · Wenkai Xu -
2019 : Invited Talk - Arthur Gretton: Relative goodness-of-fit tests for models with latent variables. »
Arthur Gretton -
2019 Poster: Learning deep kernels for exponential family densities »
Li Kevin Wenliang · D.J. Sutherland · Heiko Strathmann · Arthur Gretton -
2019 Oral: Learning deep kernels for exponential family densities »
Li Kevin Wenliang · D.J. Sutherland · Heiko Strathmann · Arthur Gretton -
2017 Poster: An Adaptive Test of Independence with Analytic Kernel Embeddings »
Wittawat Jitkrittum · Zoltan Szabo · Arthur Gretton -
2017 Talk: An Adaptive Test of Independence with Analytic Kernel Embeddings »
Wittawat Jitkrittum · Zoltan Szabo · Arthur Gretton