Variational Bayesian Inference for Bipartite Mixed-membership Stochastic Block Model with Applications to Collaborative Filtering

TL;DR

This paper introduces a novel bipartite mixed-membership stochastic block model for collaborative filtering, utilizing variational Bayesian inference to improve rating predictions in recommender systems.

Contribution

The paper develops a new network-based model with a conjugate prior and a variational Bayesian algorithm, enhancing collaborative filtering accuracy over existing methods.

Findings

The model outperforms standard SBM in simulations.

It provides more accurate inference with outlier detection.

It achieves better rating prediction on MovieLens dataset.

Abstract

Motivated by the connections between collaborative filtering and network clustering, we consider a network-based approach to improving rating prediction in recommender systems. We propose a novel Bipartite Mixed-Membership Stochastic Block Model ($\mathrm{BM}^2$) with a conjugate prior from the exponential family. We derive the analytical expression of the model and introduce a variational Bayesian expectation-maximization algorithm, which is computationally feasible for approximating the untractable posterior distribution. We carry out extensive simulations to show that $\mathrm{BM}^2$ provides more accurate inference than standard SBM with the emergence of outliers. Finally, we apply the proposed model to a MovieLens dataset and find that it outperforms other competing methods for collaborative filtering.