LEARNING GRAPHICAL MODELS WITH LIMITED OBSERVATIONS OF HIGH-DIMENSIONAL DATA by

In a variety of computational domains, the number of samples available for learn-ing remains relatively small as compared to increasing data dimensions. This is com-mon in computational biology and vision, posing even greater challenges when com-bined with complex interactions among variables. Consequently, the bias-variance trade-off requires one to invest model parameters with the utmost care for robust learning. In the small sample context, we argue for incorporating the available prior knowledge, and introducing carefully chosen biases to reduce variance. Motivated by this philosophy and particular problems from biology and vision, we propose two new generative approaches within a graphical model formalism: (a) A comprehensive statistical model for analyzing cell signaling networks, and (b) A restricted family of latent variable forest models for discovery of complex dependencies. The first method is particular to protein signaling networks, which play a central role in transcriptional regulation and the etiology of many diseases. With known molecular connections, our model is anchored to a pre-defined core signaling topology