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Bala Rajaratnam - Stanford University

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”Methods for Robust High Dimensional Graphical Model Selection”
20 March 2014 from 4:00 PM to 5:00 PM
201 Thomas Building
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Learning high dimensional correlation and partial correlation graphical network models is a topic of contemporary interest. A popular approach is to use L1 regularization methods to induce sparsity in the inverse covariance estimator, leading to sparse partial covariance/correlation graphs. Such approaches can be grouped into two classes: (1) regularized likelihood methods and (2) regularized regression-based, or pseudo-likelihood, methods. Regression based methods have the distinct advantage that they do not explicitly assume Gaussianity. One gap in the area is that none of the popular methods proposed for solving regression based objective functions have provable convergence guarantees. Hence it is not clear if resulting estimators actually yield correct partial correlation/partial covariance graphs. To this end, we propose a new regression based graphical model selection method that is both tractable and has provable convergence guarantees. In addition we also demonstrate that our approach yields estimators that have good large sample properties. The methodology is illustrated on both real and simulated data. We also present a novel unifying framework that places various pseudo-likelihood graphical model selection methods as special cases of a more general formulation, leading to important insights.(Joint work with S. Oh and K. Khare)

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