Bayesian Nonnegative Tensor Completion With Automatic Rank Determination.

Area of Science:

• Machine Learning
• Data Science
• Applied Mathematics

Background:

• Nonnegative CANDECOMP/PARAFAC (CP) factorization is crucial for nonnegative tensor completion.
• Existing models struggle with manual rank selection, leading to overfitting or underfitting.
• Probabilistic CP models can estimate rank but fail to learn nonnegative factors from incomplete data and ignore uncertainty.

Purpose of the Study:

• To propose a unified framework for nonnegative tensor completion using a fully Bayesian approach.
• To enable automatic rank determination and uncertainty estimation for nonnegative latent factors.
• To address limitations of existing methods in handling incomplete tensors and parameter selection.

Main Methods:

• Developed a fully Bayesian treatment for nonnegative tensor completion with automatic rank determination.
• Employed hierarchical sparsity-inducing priors for uncertainty estimation and low-rank structure recovery.
• Implemented two fully Bayesian inference methods for posterior estimation and a hybrid computing strategy for efficiency.

Main Results:

• The proposed model accurately recovers missing data in incomplete tensors.
• Automatic estimation of CP rank from incomplete tensors was achieved.
• Demonstrated superior performance in real-world image and video inpainting compared to state-of-the-art methods.

Conclusions:

• The fully Bayesian nonnegative tensor completion model effectively handles incomplete data and automatically determines rank.
• The approach provides uncertainty estimates for latent factors, mitigating overfitting and parameter selection issues.
• The method offers significant improvements in data recovery and inpainting tasks, with efficient computation for large datasets.