Bayesian Adaptive Tucker Decompositions for Tensor Factorization

2024-11-15

AI Summary

Tucker decomposition requires manual pre-specification of multiranks, compromising the balance between model parsimony and structural expressiveness. Method: We propose a Bayesian adaptive Tucker decomposition model featuring (i) an infinite递增收缩 prior for fully automatic, data-driven multirank inference; (ii) a local sparsity prior on the core tensor to jointly capture inter-variable dependencies and intrinsic low-dimensional structure; and (iii) unified handling of continuous/binary data with joint missing-value imputation, implemented via adaptive Gibbs sampling for computational efficiency. Contribution/Results: We establish posterior consistency theoretically. Empirical evaluation on chemometric and complex ecological datasets demonstrates substantial improvements over state-of-the-art methods in imputation accuracy, robustness, and interpretability—without requiring rank tuning.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Automatically infer latent multi-rank in Tucker decomposition
• Handle both continuous and binary incomplete multiway data
• Improve tensor factorization with Bayesian adaptive shrinkage prior

Innovation

• Bayesian adaptive Tucker decomposition model
• Infinite increasing shrinkage prior
• Efficient adaptive Gibbs sampler