Parametric inference in the large data limit using maximally informative models

Motivated by data-rich experiments in transcriptional regulation and sensory neuro-science, we consider the following general problem in statistical inference. When exposed to a high-dimensional signal S, a system of interest computes a representation R of that signal which is then observed through a noisy measurement M. From a large number of signals and measurements, we wish to infer the \"filter\" that maps S to R. However, the standard method for solving such problems, likelihood-based inference, requires perfect a priori knowledge of the \"noise function\" mapping R to M. In practice such noise functions are usually known only approximately, if at all, and using an incorrect noise funct