Classifier Design Given an Uncertainty Class of Feature Distributions via Regularized Maximum Likelihood and the...

Contemporary high-throughput technologies provide measurements of very large numbers of variables but often with very small sample sizes. This paper proposes an optimization-based paradigm for utilizing prior knowledge to design better performing classifiers when sample sizes are limited. We derive approximate expressions for the first and second moments of the true error rate of the proposed classifier under the assumption of two widely-used models for the uncertainty classes; ε-contamination and p-point classes. The applicability of the approximate expressions is discussed by defining the problem of finding optimal regularization parameters through minimizing the expected true error. Simulation results using the Zipf model show that the proposed paradigm yields improved classifiers that outperform traditional classifiers that use only training data. Our application of interest involves discrete gene regulatory networks possessing labeled steady-state distributions. Given prior operational knowledge of the process, our goal is to build a classifier that can accurately label future observations obtained in the steady state by utilizing both the available prior knowledge and the training data. We examine the proposed paradigm on networks containing NF-κB pathways, where it shows significant improvement in classifier performance over the classical data-only approach to classifier design. Companion website: http://gsp.tamu.edu/Publications/supplementary/shahrokh12a.