Bayesian Adaptive Tucker Decompositions for Tensor Factorization

TL;DR

This paper presents a Bayesian adaptive Tucker decomposition model that automatically infers the multi-rank of tensor data, improving flexibility and efficiency over traditional methods, with applications demonstrating its advantages.

Contribution

Introduces a Bayesian model with an infinite shrinkage prior for automatic multi-rank inference in Tucker tensor decomposition, supporting various data types and missing data imputation.

Findings

Outperforms existing tensor factorization methods in simulations.

Supports both continuous and binary data.

Enables effective missing data imputation.

Abstract

Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the issue of pre-selecting the latent multi-rank, we introduce a Bayesian adaptive Tucker decomposition model that infers the multi-rank automatically via an infinite increasing shrinkage prior. The model introduces local sparsity in the core tensor, inducing rich and at the same time parsimonious dependency structures. Posterior inference proceeds via an efficient adaptive Gibbs sampler, supporting both continuous and binary data and allowing for straightforward missing data imputation when dealing with incomplete multiway data. We discuss fundamental properties of the proposed modeling framework, providing theoretical justification. Simulation studies and applications to chemometrics and complex ecological data offer compelling evidence of its advantages over existing tensor factorization methods.