mlsanityData to 14 Oct 2026

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

arXiv 2412.17916 ↗First posted 23 Dec 2024stat.ML cs.LG math.OCcited by 1

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Abstract (arXiv)

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 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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 2 of its 32 references that are in the map. First posted on arXiv 23 Dec 2024.

Builds on

2 of 32 references.

References · 2

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  2. 2022Maximum Entropy on the Mean and the Cram'er Rate Function in Statistical Estimation and Inverse Problems: Properties, Models, and Algorithmscited by 2

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Citing papers per year: 2026: 1.

1 paper.

  1. 2026On the Computational and Statistical Efficiency of the Empirical Maximum Entropy on the Mean Methodcited by 0