Title: Parameterized matrix factorization with missing data via nonconvex optimization
Authors: Xiaodong Li - UC Davis (United States) [presenting]
Abstract: Matrix factorization is one of the most foundational unsupervised learning techniques due to its power in exploration of informative structures in contemporary big data sets. We are particularly interested in parameterized matrix factorization with possible missing entries. Applications include reduced rank regression with possible missing entries in the responses, collaborative filtering with side information, pairwise ranking with aggregated comparison scores, to name just a few. We aim to establish a unified methodological and theoretical framework for nonconvex optimization based parameterized matrix factorization. In particular, we aim to implement a unified local minimum analysis in understanding the adaptivity of the method to the parameterized low-rank structures. For example, in the noiseless case we aim to study how to establish the required sampling complexity for exact recovery by the intrinsic dimension of the parameters; in the noisy case we are also interested in figuring out how the local-minimum based approximation depends on both the sample complexity and the intrinsic dimension.