Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of a complex data set in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of a dependent data stream remains largely unexplored. In this talk, I will describe our recent results that show that the well-known OMF algorithm for i.i.d. stream of data proposed in Mairal et al, in fact converges almost surely to the set of critical points of the expected loss function, even when the data matrices form a Markov chain satisfying a mild mixing condition. For applications, I will demonstrate dictionary learning from a sequence of images generated by a Markov Chain Monte Carlo (MCMC) sampler and a “Network Dictionary Learning” application, which extracts `network dictionary patches' from a given network in an online manner that encodes main features of the network. This work is part of an ongoing surge of novel matrix factorization problem formulations, and with time we will describe other interesting new problems before closing the talk.

Laura Balzano is an associate professor in Electrical Engineering and Computer Science at the University of Michigan, and a member of the Institute for Advanced Study for the special year on Optimization, Statistics, and Theoretical Machine Learning. She is a recipient of the NSF Career Award, a Fulbright fellowship, ARO Young Investigator Award, AFOSR Young Investigator Award, and faculty fellowships from Intel and 3M. Laura received a BS from Rice University, MS from UCLA, and PhD from the University of Wisconsin, all in Electrical and Computer Engineering. Her main research focus is on modeling with big, messy data — highly incomplete or corrupted data, uncalibrated data, and heterogeneous data — and its applications in networks, environmental monitoring, and computer vision. Her expertise is in statistical signal processing, matrix factorization, and optimization.