2012/06/30 by Masashi Sugiyama, Sugiyama, Masashi, Takafumi Kanamori +9 · 1 citation
Computer Science · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.1207.0099
openalex publication_date 2012/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.