title: Density-difference estimation.
abstract: We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure of first estimating two densities separately and then computing their difference. However, this procedure does not necessarily work well because the first step is performed without regard to the second step, and thus a small estimation error incurred in the first stage can cause a big error in the second stage. In this letter, we propose a single-shot procedure for directly estimating the density difference without separately estimating two densities. We derive a nonparametric finite-sample error bound for the proposed single-shot density-difference estimator and show that it achieves the optimal convergence rate. We then show how the proposed density-difference estimator can be used in L²-distance approximation. Finally, we experimentally demonstrate the usefulness of the proposed method in robust distribution comparison such as class-prior estimation and change-point detection.
authors.affiliation: Tokyo Institute of Technology, Tokyo 152-8552, Japan. sugi@cs.titech.ac.jp
authors.forename: Masashi
authors.initials: M
authors.lastname: Sugiyama
authors.forename: Takafumi
authors.initials: T
authors.lastname: Kanamori
authors.forename: Taiji
authors.initials: T
authors.lastname: Suzuki
authors.forename: Marthinus Christoffel
authors.initials: MC
authors.lastname: du Plessis
authors.forename: Song
authors.initials: S
authors.lastname: Liu
authors.forename: Ichiro
authors.initials: I
authors.lastname: Takeuchi
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D001315:Australia; D057225:Data Mining / Q000706:statistics & numerical data*; D016208:Databases, Factual; D003920:Diabetes Mellitus / Q000453:epidemiology; D005858:Germany; D006801:Humans; D016015:Logistic Models; D012984:Software