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arXiv · 2306.10592

Conditional expectation using compactification operators

Suddhasattwa Das
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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.

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BibTeXRIS

Suddhasattwa Das. 2023-06-18. Conditional expectation using compactification operators. https://doi.org/10.1016/j.acha.2024.101638

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