Connecting Statistical Problems with Different Structures

Abstract

Estimating graphical models is a fundamental problem in machine learning. In many applications, the Gaussian graphical model is used where the edge structure represents the sparsity pattern of the precision matrix. Seminal works have studied the information-theoretic limits of recovering Gaussian graphical models, and today we have a near-complete picture for dense graphs and graphs of bounded degree. However, many of the networks we see in practice have power-law degree distributions. In this talk I’ll discuss recent results for the statistical limits of structure recovery in this setting and describe intriguing threshold phenomena that occur. The results are based on an interesting connection between Gaussian graphical model selection and community detection in random graphs. Based on joint work with David Gamarnik and Xinmeng Huang.

Bio

Guy Bresler is the Bonnie & Marty Tenenbaum Assistant Professor in the Department of Electrical Engineering and Computer Science at MIT. His research interests span statistics, machine learning, information theory, and algorithms. His recent work has focused on computational and statistical aspects of high-dimensional inference problems including graphical model structure learning, community detection, and mixture models. Guy received a PhD in EECS from UC Berkeley (2014), an MSc in Mathematics and Computer Science from Tel Aviv University (2009), and a BSc in Electrical Engineering from Tel Aviv University (2008). He was a Simons Institute Research Fellow (2014) and a postdoc in the Statistics Department at Stanford (2014-2015). He received the NSF CAREER award (2018), the Google Research Scholar Award (2018), the NeurIPS Best Student Paper Award (2008), and has given tutorials on his research at ICML 2017 and NeurIPS 2018. His work can be found on arXiv (http://arxiv.org/a/bresler_g_1.html).