# A Unified Framework for Stochastic Matrix Factorization via Variance Reduction

## TL;DR

This paper introduces a unified variance reduction framework for stochastic matrix factorization, significantly improving convergence speed and accuracy across various formulations through theoretical analysis and extensive experiments.

## Contribution

It presents a general framework that accelerates stochastic matrix factorization algorithms and provides non-asymptotic convergence guarantees, unifying multiple existing methods.

## Key findings

- Faster convergence compared to state-of-the-art methods
- More accurate dictionary recovery in experiments
- Theoretical bounds on convergence and complexity

## Abstract

We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a non-asymptotic convergence analysis of our framework and derive computational and sample complexities for our algorithm to converge to an $\epsilon$-stationary point in expectation. In addition, extensive experiments for a wide class of SMF formulations demonstrate that our framework consistently yields faster convergence and a more accurate output dictionary vis-\`a-vis state-of-the-art frameworks.