Least-squares two-sample test

Authors:
Masashi Sugiyama;Taiji Suzuki;Yuta Itoh;Takafumi Kanamori;Manabu Kimura
Affiliations:
Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan and PRESTO, Japan Science and Technology Agency (JST), Japan;The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan;Nagoya University, Furocho, Chikusaku, Nagoya 464-8603, Japan;Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan
Venue:
Neural Networks
Year:
2011

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Abstract

The goal of the two-sample test (a.k.a. the homogeneity test) is, given two sets of samples, to judge whether the probability distributions behind the samples are the same or not. In this paper, we propose a novel non-parametric method of two-sample test based on a least-squares density ratio estimator. Through various experiments, we show that the proposed method overall produces smaller type-II error (i.e., the probability of judging the two distributions to be the same when they are actually different) than a state-of-the-art method, with slightly larger type-I error (i.e., the probability of judging the two distributions to be different when they are actually the same).