2023/08/15 by Duc Hoan Nguyen, Nguyen, Duc Hoan, Werner Zellinger +3 · 5 citations
Computer Science · Mathematics · #68Q32 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Statistical Methods and Inference #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.2308.07887
openalex publication_date 2023/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability estimation. To address the above problem, we employ the general regularization scheme in reproducing kernel Hilbert spaces. The convergence rate of the corresponding regularized algorithm is established by taking into account both the smoothness of the derivative and the capacity of the space in which it is estimated. This is done in terms of general source conditions and the regularized Christoffel functions. We also find that the reconstruction of Radon-Nikodym derivatives at any particular point can be done with high order of accuracy. Our theoretical results are illustrated by numerical simulations.