National Science Foundation (NSF) grant CCF-1934568.

Nevertheless, instead of systematically reasoning and actively choosing informative samples, policy gradients for local search are often obtained from random perturbations. These random samples yield high variance estimates and hence are sub-optimal in terms of sample complexity.

The next point in the iteration process is defined as the minimizer of this model.

Nonnegative matrix factorization (NMF) is a popular data analysis method, the objective of which is to approximate a matrix with all nonnegative components into the product of two nonnegative matrices. In this work, we describe a new simple and efficient algorithm for multi-factor nonnegative matrix factorization (mfNMF) problem that generalizes the original NMF problem to more than two factors. Furthermore, we extend the mfNMF algorithm to incorporate a regularizer based on the Dirichlet distribution to encourage the sparsity of the components of the obtained factors. Our sparse mfNMF algorithm affords a closed form and an intuitive interpretation, and is more efficient in comparison with previous works that use fix point iterations. We demonstrate the effectiveness and efficiency of our algorithms on both synthetic and real data sets.