Abstract: Linear Gaussian covariance models are Gaussian models with linear constraints on the covariance matrix. Such models arise in many applications, such as stochastic processes from repeated time series data, Brownian motion tree models used for phylogenetic analyses, and network tomography models used for analyzing connections in the Internet. Maximum likelihood estimation in this class of models leads to a non-convex optimization problem that typically has many local maxima. Using recent results on the asymptotic distribution of the extreme eigenvalues of the Wishart distribution, we prove that maximum likelihood estimation for linear Gaussian covariance models is in fact, with high probability, concave in nature and therefore can be solved using iterative hill-climbing methods.
Bio: Caroline Uhler is an assistant professor in EECS and IDSS at MIT. She holds an MSc in Mathematics, a BSc in Biology, and an MEd in High School Mathematics Education from the University of Zurich. She obtained her PhD in Statistics from UC Berkeley in 2011. After short postdoctoral positions at the Institute for Mathematics and its Applications at the University of Minnesota and at ETH Zurich, she joined IST Austria as an assistant professor (2012-2015). Her research focuses on mathematical statistics, in particular on graphical models and the use of algebraic and geometric methods in statistics, and on applications to biology. She is an elected member of the International Statistical Institute and she received a Sofja Kovalevskaja Award from the Humboldt Foundation and a START Award from the Austrian Science Fund.