Conditional expectation using compactification operators
Abstract
The separate tasks of denoising, least squares expectation, and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a product of two random variables. This paper focuses on this more general problem and describes an operator theoretic approach to estimating the conditional expectation. Kernel integral operators are used as a compactification tool, to set up the estimation problem as a linear inverse problem in a reproducing kernel Hilbert space. This equation is shown to have solutions that allow numerical approximation, thus guaranteeing the convergence of data-driven implementations. The overall technique is easy to implement, and their successful application to some real-world problems are also shown.
Cite
@article{arxiv.2306.10592,
title = {Conditional expectation using compactification operators},
author = {Suddhasattwa Das},
journal= {arXiv preprint arXiv:2306.10592},
year = {2024}
}