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Main Authors:	King-Roskamp, Matthew, Choksi, Rustum, Hoheisel, Tim
Format:	Preprint
Published:	2024
Subjects:	Machine Learning Optimization and Control 49N15, 49N30, 90C30, 68V10
Online Access:	https://arxiv.org/abs/2412.17916
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author	King-Roskamp, Matthew Choksi, Rustum Hoheisel, Tim
author_facet	King-Roskamp, Matthew Choksi, Rustum Hoheisel, Tim
contents	We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further develop general estimates for the difference between the MEM solutions with different priors $μ$ and $ν$ based upon the epigraphical distance between their respective log-moment generating functions. These estimates allow us to establish a rate of convergence in expectation for empirical means. We illustrate our results with denoising on MNIST and Fashion-MNIST data sets.
format	Preprint
id	arxiv_https___arxiv_org_abs_2412_17916
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems King-Roskamp, Matthew Choksi, Rustum Hoheisel, Tim Machine Learning Optimization and Control 49N15, 49N30, 90C30, 68V10 We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further develop general estimates for the difference between the MEM solutions with different priors $μ$ and $ν$ based upon the epigraphical distance between their respective log-moment generating functions. These estimates allow us to establish a rate of convergence in expectation for empirical means. We illustrate our results with denoising on MNIST and Fashion-MNIST data sets.
title	Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems
topic	Machine Learning Optimization and Control 49N15, 49N30, 90C30, 68V10
url	https://arxiv.org/abs/2412.17916

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