Information Theoretic Model Selection for Pattern Analysis

Exploratory data analysis requires (i) to define a set of patterns hypothesized to exist in the data, (ii) to specify a suitable quantification principle or cost function to rank these patterns and (iii) to validate the inferred patterns. For data clustering, the patterns are object partitionings into k groups; for PCA or truncated SVD, the patterns are orthogonal transformations with projections to a low-dimensional space. We propose an information theoretic principle for model selection and model-order selection. Our principle ranks competing pattern cost functions according to their ability to extract context sensitive information from noisy data with respect to the chosen hypothesis class. Sets of approximative solutions serve as a basis for a communication protocol. Analogous to Buhmann (2010), inferred models maximize the so-called approximation capacity that is the mutual information between coarsened training data patterns and coarsened test data patterns. We demonstrate how to apply our validation framework by the well-known Gaussian mixture model and by a multi-label clustering approach for role mining in binary user privilege assignments.