Papers › Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems
Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems
Matthew King-Roskamp, Rustum Choksi, Tim Hoheisel
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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