Bayesian Robust Tensor Factorization for Incomplete Multiway Data

TL;DR

This paper introduces a Bayesian model for robust tensor factorization that effectively handles missing data and outliers, automatically determines model complexity, and scales efficiently to large datasets.

Contribution

It presents a novel Bayesian framework for tensor factorization that automatically infers tensor rank and sparsity, improving robustness and scalability over existing methods.

Findings

Outperforms state-of-the-art algorithms on synthetic and real datasets.

Automatically discovers the true tensor rank and outlier sparsity.

Scales linearly with data size and prevents overfitting.

Abstract

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor capturing the local information (also considered as outliers), thus providing the robust predictive distribution over missing entries. The low-CP-rank tensor is modeled by multilinear interactions between multiple latent factors on which the column sparsity is enforced by a hierarchical prior, while the sparse tensor is modeled by a hierarchical view of Student-$t$ distribution that associates an individual hyperparameter with each element independently. For model learning, we develop an efficient closed-form variational inference under a fully Bayesian treatment, which can effectively prevent the overfitting problem and scales linearly with data size. In contrast to existing related works, our method can perform model selection automatically and implicitly without need of tuning parameters. More specifically, it can discover the groundtruth of CP rank and automatically adapt the sparsity inducing priors to various types of outliers. In addition, the tradeoff between the low-rank approximation and the sparse representation can be optimized in the sense of maximum model evidence. The extensive experiments and comparisons with many state-of-the-art algorithms on both synthetic and real-world datasets demonstrate the superiorities of our method from several perspectives.