Density-Difference Estimation
  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. 
Masashi Sugiyama, Takafumi Kanamori, Taiji Suzuki, Marthinus   Christoffel du Plessis, Song Liu, Ichiro Takeuchi
cs.LG stat.ML