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Activity Number: 163 - Methods for Complex Data: The Next Generation
Type: Topic Contributed
Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
Sponsor: Business and Economic Statistics Section
Abstract #302880
Title: Learning Local Dependence in Ordered Data
Author(s): Guo Yu* and Jacob Bien
Companies: University of Washington and University of Southern California
Keywords: Local dependence; Gaussian graphical models; precision matrices; holesky factor; hierarchical group lasso

In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant neighborhood size unrealistic. We propose a framework for learning this local dependence based on estimating the inverse of the Cholesky factor of the covariance matrix. Penalized maximum likelihood estimation of this matrix yields a simple regression interpretation for local dependence in which variables are predicted by their neighbors. Our proposed method involves solving a convex, penalized Gaussian likelihood problem with a hierarchical group lasso penalty. The problem decomposes into independent subproblems which can be solved efficiently in parallel using first-order methods. Our method yields a sparse, symmetric, positive definite estimator of the precision matrix, encoding a Gaussian graphical model. We derive theoretical results not found in existing methods attaining this structure. Empirical results show our method performing favorably compared to existing methods.

Authors who are presenting talks have a * after their name.

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