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

Matthew King-Roskamp, Rustum Choksi, Tim Hoheisel
12/23/2024
stat.MLcs.LGmath.OC

No official code found. Best implementation: mattkingros/MEM-Denoising-and-Deblurring (0 stars, last commit 2024-12-23).

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 $μ$ 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.

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Cite this paper

@article{kingroskamp2024datadriven,
  title  = {Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems},
  author = {Matthew King-Roskamp and Rustum Choksi and Tim Hoheisel},
  year   = {2024},
  eprint = {2412.17916},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2412.17916v1}
}

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