Conditional expectation using compactification operators

• URL: http://arxiv.org/abs/2306.10592v4
• Date: Mon, 8 Jan 2024 15:49:33 GMT
• Title: Conditional expectation using compactification operators
• Authors: Suddhasattwa Das
• Abstract summary: This paper 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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