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Learning Kernel Tests Without Data Splitting
Jonas Kübler · Wittawat Jitkrittum · Bernhard Schölkopf · Krikamol Muandet

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #891

Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While data splitting results in a tractable null distribution, it suffers from a reduction in test power due to smaller test sample size. Inspired by the selective inference framework, we propose an approach that enables learning the hyperparameters and testing on the full sample without data splitting. Our approach can correctly calibrate the test in the presence of such dependency, and yield a test threshold in closed form. At the same significance level, our approach’s test power is empirically larger than that of the data-splitting approach, regardless of its split proportion.

Author Information

Jonas Kübler (MPI for Intelligent Systems, Tübingen)
Wittawat Jitkrittum (Google Research)

Wittawat Jitkrittum is a postdoctoral researcher at Max Planck Institute for Intelligent Systems, Germany. He earned his PhD from Gatsby Unit, University College London with a thesis on informative features for comparing distributions. He received a best paper award at NeurIPS 2017 and the ELLIS PhD award 2019 for outstanding dissertation. Wittawat has broad research interests covering kernel methods, deep generative models, and approximate Bayesian inference. He served as a publication chair for AISTATS 2016, a program committee for NeurIPS, ICML, AISTATS, among others, and is a co-organizer of the first Southeast Asia Machine Learning School (SEAMLS 2019) in Indonesia and a co-organizer of the first Machine Learning Research School (MLRS 2019) in Thailand.

Bernhard Schölkopf (MPI for Intelligent Systems, Tübingen)

Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.

Krikamol Muandet (Max Planck Institute for Intelligent Systems)

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