Data-Driven Methods for Sparse Network Estimation

Seminar | April 19 | 3-4 p.m. | 3110 Etcheverry Hall

 Somayeh Sojoudi, Assistant Project Scientist, University of California, Berkeley

 Electrical Engineering and Computer Sciences (EECS), Department of Mechanical Engineering (ME)

System identification is a fundamental area in control theory, which is concerned with finding mathematical models of dynamical systems from data. As a special case of this area, the problem of finding the underlying network structure of a system from measured data is of interest in many areas. This problem can be addressed through the notion of graphical models, which aims to capture the relationships between the parameters of a system using graphs. Graphical models have applications in many areas, such as social sciences, robotics, biology, neuroscience, and power systems. Learning graphical models is often challenged by the fact that only a small number of samples are available. Despite the popularity of graphical lasso for solving this problem, there is not much known about the properties of this statistical method as an optimization algorithm. In this talk, we will develop new notions of sign-consistent matrices and inverse-consistent matrices to obtain key properties of graphical lasso. In particular, we will prove that although the complexity of solving graphical lasso is high, the sparsity pattern of its solution has a simple formula if a sparse graphical model is sought. Besides graphical lasso, there are several techniques for learning graphical models. We will design an optimization-based mathematical framework to compare the performance of various techniques and find the best one for each application. We will illustrate our results in different case studies.

Somayeh Sojoudi is an Assistant Project Scientist at the University of California, Berkeley. She received her PhD degree in Control & Dynamical Systems from California Institute of Technology in 2013. She was an Assistant Research Scientist at New York University School of Medicine from 2013 to 2015. She has worked on several interdisciplinary problems in optimization theory, control theory, machine learning, data analytics, and power systems. Somayeh Sojoudi is an associate editor for the IEEE Transactions on Smart Grid. She is a co-recipient of the 2015 INFORMS Optimization Society Prize for Young Researchers and a co-recipient of the 2016 INFORMS ENRE Energy Best Publication Award. She is a co-author of a best student paper award finalist for the 53rd IEEE Conference on Decision and Control 2014., 510-642-5867