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Density-Difference Estimation
Masashi Sugiyama · Takafumi Kanamori · Taiji Suzuki · Marthinus C du Plessis · Song Liu · Ichiro Takeuchi

Mon Dec 03 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor

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, such a two-step 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 paper, we propose a single-shot procedure for directly estimating the density difference without separately estimating two densities. We derive a non-parametric 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 utilized 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.

Author Information

Masashi Sugiyama (RIKEN / University of Tokyo)
Takafumi Kanamori (Nagoya University)
Taiji Suzuki (The University of Tokyo/RIKEN-AIP)
Marthinus C du Plessis (Tokyo Institute of Technology)
Song Liu (Tokyo Institute of Technology)
Ichiro Takeuchi (Nagoya Institute of Technology)

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