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Bayesian MMSE estimation of classification error and performance on real genomic data

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2 Author(s)
Dalton, L.A. ; Dept. of Electr. & Comput. Eng., Texas A&M Univ., College Station, TX, USA ; Dougherty, E.R.

Small sample classifier design has become a major issue in the biological and medical communities, owing to the recent development of high-throughput genomic and proteomic technologies. And as the problem of estimating classifier error is already handicapped by limited available information, it is further compounded by the necessity of reusing training-data for error estimation. Due to the difficulty of error estimation, all currently popular techniques have been heuristically devised, rather than rigorously designed based on statistical inference and optimization. However, a recently proposed error estimator has placed the problem into an optimal mean-square error (MSE) signal estimation framework in the presence of uncertainty. This results in a Bayesian approach to error estimation based on a parameterized family of feature-label distributions. These Bayesian error estimators are optimal when averaged over a given family of distributions, unbiased when averaged over a given family and all samples, and analytically address a trade-off between robustness (modeling assumptions) and accuracy (minimum mean-square error). Closed form solutions have been provided for two important examples: the discrete classification problem and linear classification of Gaussian distributions. Here we discuss the Bayesian minimum mean-square error (MMSE) error estimator and demonstrate performance on real biological data under Gaussian modeling assumptions.

Published in:

Genomic Signal Processing and Statistics (GENSIPS), 2010 IEEE International Workshop on

Date of Conference:

10-12 Nov. 2010