Density-Difference Estimation
This addresses a fundamental statistical estimation problem for researchers and practitioners in machine learning and data analysis, offering a more robust alternative to existing methods.
The paper tackles the problem of estimating the difference between two probability densities by proposing a single-shot method that directly estimates the density difference, avoiding the error amplification of two-step approaches, and achieves the optimal convergence rate with experimental validation.
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.