Online matrix factorization for Markovian data

Hanbaek Lyu, Deanna Needell, and I recently had a manuscript published at JMLR: “Online matrix factorization for Markovian data and applications to Network Dictionary Learning.” In this work we show that the well-known OMF algorithm for i.i.d. stream of data converges almost surely to the set of critical points of the expected loss function, even when the data stream is dependent but Markovian. It would be of great interest to show that this algorithm further converges to global minimizers, as has been recently proven for many batch-processing algorithms. We are excited about this important step, generalizing the theory for the more practical case where the data aren’t i.i.d. Han’s work applying this to network sampling is super cool — and in fact it’s impossible to sample a sparse network in an i.i.d. way, so this extension is critical for this application. Han is on the academic job market this year.