Bayesian Robust Tensor Factorization for Incomplete Multiway Data.

Area of Science:

• Machine Learning
• Data Science
• Tensor Decomposition

Background:

• Tensor factorization methods often struggle with incomplete datasets and noisy entries.
• Existing approaches require manual parameter tuning for optimal performance.

Purpose of the Study:

• To develop a robust generative model for tensor factorization that handles missing data and outliers.
• To enable automatic model selection and outlier detection without parameter tuning.

Main Methods:

• Proposes a generative model to infer a low-rank tensor and a sparse outlier tensor.
• Employs a hierarchical prior for the low-rank component and a hierarchical Student-t distribution for the sparse component.
• Utilizes efficient variational inference within a fully Bayesian framework for model learning.

Main Results:

• The model automatically determines the CANDECOMP/PARAFAC (CP)-rank and adapts to various outlier types.
• Achieves robust predictions on missing entries by balancing low-rank approximation and sparse representation.
• Demonstrates superior performance over state-of-the-art methods on synthetic and real-world datasets.

Conclusions:

• The proposed generative model offers a robust and automated solution for tensor factorization with missing data and outliers.
• The fully Bayesian variational inference approach prevents overfitting and scales linearly with data size.
• This method advances tensor analysis by providing accurate predictions and inherent model selection capabilities.