Loss-Based Estimation with Cross-Validation: Applications to Microarray Data Analysis and Motif Finding

Current statistical inference problems in genomic data analysis involve parameter estimation for high-dimensional multivariate distributions, with typically unknown and intricate correlation patterns among variables. Addressing these inference questions satisfactorily requires: (i) an intensive and thorough search of the parameter space to generate good candidate estimators, (ii) an approach for selecting an optimal estimator among these candidates, and (iii) a method for reliably assessing the performance of the resulting estimator. We propose a unified loss-based methodology for estimator construction, selection, and performance assessment with cross-validation. In this approach, the parameter of interest is defined as the risk minimizer for a suitable loss function and candidate estimators are generated using this (or possibly another) loss function. Cross-validation is applied to select an optimal estimator among the candidates and to assess the overall performance of the resulting estimator. This general estimation framework encompasses a number of problems which have traditionally been treated separately in the statistical literature, including multivariate outcome prediction and density estimation based on either uncensored or censored data. This article provides an overview of the methodology and describes its application to two problems in genomic data analysis: the prediction of biological and clinical outcomes (possibly censored) using microarray gene expression measures and the identification of regulatory motifs (i.e., transcription factor binding sites) in DNA sequences.