Parametric Inference in the Large Data Limit Using Maximally Informative Models

Kinney, J. B., Atwal, G. S. (January 2014) Parametric Inference in the Large Data Limit Using Maximally Informative Models. Neural Comput, 26 (4). pp. 637-653. ISSN 0899-7667

DOI: 10.1162/NECO_a_00568


Motivated by data-rich experiments in transcriptional regulation and sensory neuroscience, 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 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 likelihood-based inference.

Item Type: Paper
Subjects: bioinformatics
bioinformatics > quantitative biology
CSHL Authors:
Communities: CSHL Cancer Center Program > Gene Regulation and Cell Proliferation
CSHL labs > Atwal lab
CSHL labs > Kinney lab
CSHL Cancer Center Program > Cancer Genetics
Depositing User: Matt Covey
Date: 30 January 2014
Date Deposited: 07 Feb 2014 21:49
Last Modified: 15 Oct 2015 15:38
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