Kinney, J. B., Atwal, G. S. (2013) Parametric inference in the large data limit using maximally informative models. Arxiv. (Unpublished)

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Abstract
Motivated by datarich experiments in transcriptional regulation and sensory neuroscience, we consider the following general problem in statistical inference. When exposed to a highdimensional 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, likelihoodbased 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 function will typically bias the inferred filter. Here we show that, in the large data limit, this need for a precharacterized noise function can be circumvented by searching for filters that instead maximize the mutual information I[M;R] between observed measurements and predicted representations. Moreover, if the correct filter lies within the space of filters being explored, maximizing mutual information becomes equivalent to simultaneously maximizing every dependence measure that satisfies the Data Processing Inequality. It is important to note that maximizing mutual information will typically leave a small number of directions in parameter space unconstrained. We term these directions "diffeomorphic modes" and present an equation that allows these modes to be derived systematically. The presence of diffeomorphic modes reflects a fundamental and nontrivial substructure within parameter space, one that is obscured by standard likelihoodbased inference.
Item Type:  Paper 

Subjects:  bioinformatics bioinformatics > computational biology bioinformatics > computational biology > statistical analysis 
CSHL Authors:  
Communities:  CSHL labs > Atwal lab CSHL labs > Kinney lab 
Depositing User:  Matt Covey 
Date:  2013 
Date Deposited:  13 May 2015 18:58 
Last Modified:  13 May 2015 18:58 
URI:  http://repository.cshl.edu/id/eprint/31501 
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