In this paper, we introduce the minimum dynamic discrimination information (MDDI) approach to probability modeling. The MDDI model relative to a given distribution G is that which has least Kullback-Leibler information discrepancy relative to G, among all distributions satisfying some information constraints given in terms of residual moment inequalities, residual moment growth inequalities, or hazard rate growth inequalities. Our results lead to MDDI characterizations of many well-known lifetime models and to the development of some new models. Dynamic information constraints that characterize these models are tabulated. A result for characterizing distributions based on dynamic Rényi information divergence is also given.

DNA microarray technology has made it possible to simultaneously measure the expression levels of tens of thousands of genes. In this paper, we address the problem of class discovery which involves unsupervised clustering of tissue samples based on corresponding gene expression data. Non-negative matrix factorization (NMF) by multiplicative updates algorithm is a powerful method for decomposing the gene expression matrix V into two matrices with nonnegative entries, V ~ WH, where each column of W defines a metagene and each column of H represents the metagene expression pattern of the corresponding sample. We describe a method for class discovery and dimensionality reduction using NMF, based on various measures of distance between two non-negative matrices. Our approach provides a unique framework for class discovery. We demonstrate the applicability of this method using cancer microarray as well as simulated data.