5 accepted papers
We develop an optimal primal-dual first-order algorithm for a class of stochastic three-composite convex minimization problems. The convergence rate of our method not only improves upon the existing methods, but also matches a lower bound derived for all first-order methods that solve this problem.…
We develop a primal-dual convex minimization framework to solve a class of stochastic convex three-composite problem with a linear operator. We consider the cases where the problem is both convex and strongly convex and analyze the convergence of the proposed algorithm in both cases. In addition, we…
The multiplicative update (MU) algorithm has been used extensively to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizations. However, theoretical convergence guarantees have only been derived for a few spe…
We develop a unified and systematic framework for performing online nonnegative matrix factorization under a wide variety of important divergences. The online nature of our algorithms makes them particularly amenable to large-scale data. We prove that the sequence of learned dictionaries converges…
We propose an optimization framework for performing online Non-negative Matrix Factorization (NMF) in the presence of outliers, based on l\ regularization and stochastic approximation. Due to the online nature of the algorithm, the proposed method has extremely low computational and storage complexi…