Conditional expectation using compactification operators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866910330039304192 |
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| author | Das, Suddhasattwa |
| author_facet | Das, Suddhasattwa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10592 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conditional expectation using compactification operators Das, Suddhasattwa Machine Learning Functional Analysis Probability 46E27, 46E22, 62G07, 62G05 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. |
| title | Conditional expectation using compactification operators |
| topic | Machine Learning Functional Analysis Probability 46E27, 46E22, 62G07, 62G05 |
| url | https://arxiv.org/abs/2306.10592 |