Estimating covariance matrices with linear structures
Mittwoch, 11. Juli 2018
15.15 – 16.45 Uhr
University of Konstanz, C427
Caroline Uhler, MIT
This event is organised by Roxana Halbleib (Research Fellow/Dept. of Economics).
About the Speaker
Caroline Uhler is Assistant Professor at the Department of Electrical Engineering and Computer Science and Institute for Data, Systems and Society, MIT. She holds an MSc in mathematics, a BSc in biology and an MEd in mathematics from the University of Zurich. She obtained her PhD in statistics from UC Berkeley. Before joining MIT, she spent a semester as a research fellow within the "Big Data" program at the Simons Institute at UC Berkeley. She also had two postdoctoral positions at the Institute of Mathematics and Its Applications (IMA) and at ETH Zurich and she was 3 years assistant professor at IST Austria.
Applications to time series analysis led T.W. Anderson to study the problem of estimating covariance matrices with linear structures. Maximum likelihood estimation for Gaussian models with linear constraints on the covariance matrix leads to a non-convex optimization problem that typically has many local maxima. Current methods for parameter estimation are based on heuristics with no guarantees. I will present efficient algorithms and explain how to initiate the algorithms in a data-informed way to obtain provable guarantees for parameter estimation in this model class. Next, we study Gaussian models that are multivariate totally positive of order two (MTP2), a model class that is given by linear constraints on the inverse covariance matrix. We show that maximum likelihood estimation under MTP2 implies sparsity without the need of a tuning parameter. Moreover, we show that the MLE always exists even in the high-dimensional setting. These properties make MTP2 constraints an intriguing alternative to methods for learning sparse graphical models such as the graphical lasso.