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• W1599313488 abstract "The design and analysis of complexity-reducedrepresentations for multivariate data is important in manyscientific and engineering domains. This thesis explores suchrepresentations from two different perspectives: deriving andanalyzing performance measures for learning tree-structuredgraphical models and salient feature subset selection fordiscrimination. Graphical models have proven to be a flexible classof probabilistic models for approximating high-dimensional data.Learning the structure of such models from data is an importantgeneric task. It is known that if the data are drawn fromtree-structured distributions, then the algorithm of Chow and Liu(1968) provides an efficient algorithm for finding the tree thatmaximizes the likelihood of the data. We leverage this algorithmand the theory of large deviations to derive the error exponent ofstructure learning for discrete and Gaussian graphical models. Wedetermine the extremal tree structures for learning, that is, thestructures that lead to the highest and lowest exponents. We provethat the star minimizes the exponent and the chain maximizes theexponent, which means that among all unlabeled trees, the star andthe chain are the worst and best for learning respectively. Theanalysis is also extended to learning foreststructured graphicalmodels by augmenting the Chow-Liu algorithm with a thresholdingprocedure. We prove scaling laws on the number of samples and thenumber variables for structure learning to remain consistent inhigh-dimensions. The next part of the thesis is concerned withdiscrimination. We design computationally efficient tree-basedalgorithms to learn pairs of distributions that are specificallyadapted to the task of discrimination and show that they performwell on various datasets vis-`a-vis existing tree-based algorithms.We define the notion of a salient set for discrimination usinginformation-theoretic quantities and derive scaling laws on thenumber of samples so that the salient set can be recoveredasymptotically." @default.
• W1599313488 created "2016-06-24" @default.
• W1599313488 creator A5058345431 @default.
• W1599313488 date "2011-01-01" @default.
• W1599313488 modified "2023-09-24" @default.
• W1599313488 title "Large-deviation analysis and applications Of learning tree-structured graphical models" @default.
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