Online Change-point Detection in High Dimensional Gaussian Graphical Models

Tuesday, November 28, 2017 - 1:25pm - 2:25pm
Lind 409
Hossein Keshavarz (University of Minnesota, Twin Cities)
Abstract: High dimensional sparse Gaussian Graphical models are widely used for analyzing large collection of random variables interconnected by a complex dependency network, arising in many problems in biology, economics, and social sciences. Increasing availability of time evolving data sets has accentuated the need for developing models for time varying networks. Piece-wise stationary graphical models, also known as change-point models, are versatile tools for modeling time evolving high dimensional networks. The primary focus of literature is on offline detection of a single abrupt change in a large sparse network. However in the online change-point detection regime, which is motivated by applications in sensor networks and financial markets, detection and collection of new samples run concurrently and the goal is to find sudden changes with the smallest delay after it occurs. In this work, we introduce a novel scalable online algorithm for detecting sudden changes in the dependency structure of sparse Gaussian Graphical models. The proposed algorithm, which is based on the conditional log-likelihood of the network, can be extended to a large class of continuous and discrete graphical models. We also investigate the statistical performance guarantees of our algorithm in various change-point scenarios.