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

arXiv: https://arxiv.org/abs/2412.17916 · HTML: https://mlsanity.com/paper/2412.17916/

## Key facts

- Cited by 1 papers 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 (most cited first, 2 of 2)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Maximum Entropy on the Mean and the Cram'er Rate Function in Statistical Estimation and Inverse Problems: Properties, Models, and Algorithms](https://mlsanity.com/paper/2211.05205/) (2022)

## Built on by (most cited first, 1 of 1)

- [On the Computational and Statistical Efficiency of the Empirical Maximum Entropy on the Mean Method](https://mlsanity.com/paper/2608.27705/) (2026)

## 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.