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Activity Number: 74
Type: Contributed
Date/Time: Sunday, July 31, 2016 : 4:00 PM to 5:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #321391
Title: Blessing of Massive Scale: Spatial Graphical Model Estimation with a Total Cardinality Constraint Approach
Author(s): Ethan Fang* and Han Liu and Mendi Wang
Companies: Princeton and Princeton and Princeton
Keywords: graphical models ; L0-Constrained ; nonconvex combinatorial optimization

We consider the problem of estimating high dimensional spatial graphical models with a total cardinality constraint (i.e., the L0-constraint). Though this problem is highly nonconvex, we show that its primal-dual gap diminishes linearly with the dimensionality and provide a convex geometry justification of this `'blessing of massive scale" phenomenon. Motivated by this result, we propose an efficient algorithm to solve the dual problem (which is concave) and prove that the solution achieves optimal statistical properties. Extensive numerical results are also provided.

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

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