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arXiv · 1207.0099

Density-Difference Estimation

Masashi Sugiyama·Takafumi Kanamori·Taiji Suzuki·Marthinus Christoffel du Plessis·Song Liu·Ichiro Takeuchi
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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, 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 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. The usefulness of the proposed method is also demonstrated experimentally.

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Masashi Sugiyama, Takafumi Kanamori, Taiji Suzuki, Marthinus Christoffel du Plessis, Song Liu, Ichiro Takeuchi. 2012-06-30. Density-Difference Estimation. https://arxiv.org/abs/1207.0099

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