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arXiv · 2412.17916

Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems

Matthew King-Roskamp·Rustum Choksi·Tim Hoheisel
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Abstract

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 $\mu$ and $\nu$ 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.

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Matthew King-Roskamp, Rustum Choksi, Tim Hoheisel. 2024-12-23. Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems. https://arxiv.org/abs/2412.17916

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