Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination

Abstract

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank. In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

Cited by in corpus (74)

• Efficient tensor completion for color image and video recovery: Low-rank tensor train
• Tensor Ring Decomposition
• Smooth PARAFAC Decomposition for Tensor Completion
• Bayesian Temporal Factorization for Multidimensional Time Series Prediction
• Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
• Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data
• Tensor Methods in Computer Vision and Deep Learning
• Guaranteed Tensor Recovery Fused Low-rankness and Smoothness
• Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modeling
• Deep Plug-and-play Prior for Low-rank Tensor Completion
• Bayesian Low Rank Tensor Ring Model for Image Completion
• Robust Low-Rank Tensor Ring Completion
• Provable Tensor Ring Completion
• Phased Array-Based Sub-Nyquist Sampling for Joint Wideband Spectrum Sensing and Direction-of-Arrival Estimation
• Tensor Computation: A New Framework for High-Dimensional Problems in EDA
• Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion
• Brain-Computer Interface with Corrupted EEG Data: A Tensor Completion Approach
• Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations
• Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way
• An Iterative Reweighted Method for Tucker Decomposition of Incomplete Multiway Tensors
• Tensor-based Basis Function Learning for Three-dimensional Sound Speed Fields
• Tensor Train Factorization and Completion under Noisy Data with Prior Analysis and Rank Estimation
• When Unsupervised Domain Adaptation Meets Tensor Representations
• Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Function
• Canonical Polyadic Decomposition with Auxiliary Information for Brain Computer Interface
• Bayesian Tensorized Neural Networks with Automatic Rank Selection
• Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion
• Nearest Neighbors for Matrix Estimation Interpreted as Blind Regression for Latent Variable Model
• Scalable Bayesian Non-Negative Tensor Factorization for Massive Count Data
• Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition
• A Lightweight Method for Modeling Confidence in Recommendations with Learned Beta Distributions
• Manifold Modeling in Embedded Space: A Perspective for Interpreting Deep Image Prior
• A generalizable framework for low-rank tensor completion with numerical priors
• Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains
• Variational Bayesian Inference for Robust Streaming Tensor Factorization and Completion
• Low-rank Tensor Grid for Image Completion
• Beyond Low Rank: A Data-Adaptive Tensor Completion Method
• Adaptive Learning of Tensor Network Structures
• Fast algorithms for Higher-order Singular Value Decomposition from incomplete data
• Quantum-Inspired Hamiltonian Monte Carlo for Bayesian Sampling
• Bayesian Tensor Network with Polynomial Complexity for Probabilistic Machine Learning
• Alternating minimization algorithms for graph regularized tensor completion
• Tensor Recovery from Noisy and Multi-Level Quantized Measurements
• Tensor Graphical Model: Non-convex Optimization and Statistical Inference
• A Unified Framework for Coupled Tensor Completion
• Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regression
• Long-Short Term Spatiotemporal Tensor Prediction for Passenger Flow Profile
• Bayesian Methods in Tensor Analysis
• Concatenated image completion via tensor augmentation and completion
• Incremental Bayesian tensor learning for structural monitoring data imputation and response forecasting
• Tuning Free Rank-Sparse Bayesian Matrix and Tensor Completion with Global-Local Priors
• Tensor completion using enhanced multiple modes low-rank prior and total variation
• Prediction of multi-dimensional spatial variation data via Bayesian tensor completion
• Deep Markov Spatio-Temporal Factorization
• Dictionary Learning with Low-rank Coding Coefficients for Tensor Completion
• Low-Rank and Sparse Enhanced Tucker Decomposition for Tensor Completion
• T-SVD Based Non-convex Tensor Completion and Robust Principal Component Analysis
• Variational Bayesian inference for CP tensor completion with side information
• Non-recurrent Traffic Congestion Detection with a Coupled Scalable Bayesian Robust Tensor Factorization Model
• Low-Rank Tensor Decomposition-Aided Channel Estimation for Millimeter Wave MIMO-OFDM Systems
• High-Dimensional Uncertainty Quantification via Tensor Regression with Rank Determination and Adaptive Sampling
• Efficient MCMC Sampling for Bayesian Matrix Factorization by Breaking Posterior Symmetries
• Spatio-Temporal Tensor Sketching via Adaptive Sampling
• Tensor Methods for Generating Compact Uncertainty Quantification and Deep Learning Models
• An Efficient Tensor Completion Method via New Latent Nuclear Norm
• Multi-Tensor Network Representation for High-Order Tensor Completion
• Low-rank quaternion tensor completion for recovering color videos and images
• Probabilistic Latent Factor Model for Collaborative Filtering with Bayesian Inference
• MiSC: Mixed Strategies Crowdsourcing
• Casewise and Cellwise Robust Multilinear Principal Component Analysis
• Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recovery
• Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes
• Multi-tensor Completion for Estimating Missing Values in Video Data
• Spectral Compressed Sensing via CANDECOMP/PARAFAC Decomposition of Incomplete Tensors