SEMINAR: "Large-scale Inference of Time-varying Markov Random Fields: Bridging the Gap Between Statistical and Computational Efficiencies" — Salar Fattahi
WHEN: December 3, 2020 3:00 pm-4:00 pm
The Departmental Seminar Series is open to all. U-M Industrial and Operations Engineering graduate students and faculty are especially encouraged to attend.
This event will be a joint seminar with the MICDE.
Large-scale Inference of Time-varying Markov Random Fields: Bridging the Gap Between Statistical and Computational Efficiencies
Contemporary systems are comprised of a massive number of interconnected components that interact according to a hierarchy of complex, dynamic, and unknown topologies. For example, with billions of neurons and hundreds of thousands of voxels, the human brain is considered as one of the most complex physiological networks, whose structure remains as a long-standing mystery. As another example, the emergence of self-driving cars has only accentuated the need for the development of real-time and reliable methods for detecting moving objects, whose temporal locations are captured through a dynamically-evolving 3D network. Nonetheless, the vast amounts of parameters to be estimated, caused both by the large number of components and the time-varying nature of the systems, are currently the major bottlenecks in our ability to successfully solve such inference problems.
The temporal behavior of today's interconnected systems can be captured via time-varying Markov random fields (MRF). A popular approach to achieve this goal is based on the so-called maximum-likelihood estimation (MLE): to find a probabilistic graphical model, based on which the observed data is most probable to occur. The MLE-based methods suffer from several fundamental drawbacks which render them impractical in realistic settings. First, they often suffer from notoriously high computational cost in the massive problems, where the number of variables to be inferred is in the order of millions, or more. Second, they fail to efficiently incorporate prior structural information into their estimation procedure. With the goal of bridging this knowledge gap, the aim of this work is to revisit the standard MLE as the “Holy Grail” of the inference methods for graphical models, and precisely pinpoint and remedy the scenarios where it fails. A recurring theme in our proposed approach is a class of efficiently-solvable mixed-integer optimization problems that is used in lieu of the regularized MLE for the inference of time-varying MRFs. Our proposed optimization problems enjoy strong statistical and computational guarantees, while being amenable to a wide class of graphical models with different side information, such as sparsity, smoothness, etc.
Salar Fattahi is an Assistant Professor in the Department of Industrial and Operations Engineering at the University of Michigan. He received his M.S. and Ph.D. degrees in Industrial Engineering and Operations Research from UC Berkeley. He received a M.S. degree from Columbia University, and a B.S. degree from Sharif University of Technology, Iran, both in Electrical Engineering. Salar’s research lies at the intersection of optimization, data analytics, and control theory. He was the recipient of several awards, including the 2020 INFORMS ENRE Best Student Paper Award, 2018 INFORMS Data Mining Best Paper Award and 2020 Power & Energy Society General Meeting Best-of-the-Best Paper Award. He was also a finalist for the 2018 American Control Conference Best Paper Award.