Making Tensor Factorizations Robust to Non-Gaussian Noise

TL;DR

This paper introduces a robust tensor factorization method that uses an L1-norm loss function to effectively handle non-Gaussian noise, improving the reliability of CP tensor decompositions in noisy environments.

Contribution

It proposes a novel L1-norm based loss function and an efficient algorithm for robust CP tensor factorization under non-Gaussian noise conditions.

Findings

L1-norm loss improves robustness to non-Gaussian noise

Algorithm effectively fits CP models with non-Gaussian perturbations

Demonstrates increased stability over traditional least squares methods

Abstract

Tensors are multi-way arrays, and the Candecomp/Parafac (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of i.i.d. Gaussian noise. We demonstrate that this loss function can actually be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization algorithm for fitting a CP model using our proposed loss function.