"Nonparametric Graphical Models"

Abstract:

Graphical modeling has proven to be an extremely useful abstraction in statistical machine learning.  The space of possible graphical models is enormous, yet only a very limited set of models has been extensively developed for continuous data.  The most basic, classical example is the Gaussian graphical model, where the precision matrix encodes the independence graph.  While Gaussian graphical models can be useful, a reliance on exact normality is limiting.  We present recent work for estimating nonparametric graphical models.  One approach is something we call "the nonparanormal," which uses copula methods to transform the variables by nonparametric functions, relaxing the strong distributional assumptions made by the Gaussian graphical model.  Another approach is to restrict the family of allowed graphs to spanning forests, enabling the use of fully nonparametric density estimation.  The resulting methods are easy to understand, simple to use, theoretically well supported, and effective for modeling of high dimensional data.  Joint work with Anupam Gupta, Han Liu, Larry Wasserman, and Min Xu.

Bio:

John Lafferty is a professor in the Computer Science Department and the Machine Learning Department within the School of Computer Science at Carnegie Mellon University, where he also holds a joint appointment in the Department of Statistics.  His research interests are in text analysis, machine learning, and statistical learning theory, with a recent focus on theory and methods for high dimensional data.

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