Scalable Bayesian Tensor Ring Factorization for Multiway Data Analysis
Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates and an effective approach for automatically adapting the tensor ring rank during the learning process. However, previous BTR method employs an Automatic Relevance Determination (ARD) prior, which can lead to sub-optimal solutions. Besides, it solely focuses on continuous data, whereas many applications involve discrete data. More importantly, it relies on the Coordinate-Ascent Variational Inference (CAVI) algorithm, which is inadequate for handling large tensors with extensive observations. These limitations greatly limit its application scales and scopes, making it suitable only for small-scale problems, such as image/video completion. To address these issues, we propose a novel BTR model that incorporates a nonparametric Multiplicative Gamma Process (MGP) prior, known for its superior accuracy in identifying latent structures. To handle discrete data, we introduce the P\'olya-Gamma augmentation for closed-form updates. Furthermore, we develop an efficient Gibbs sampler for consistent posterior simulation, which reduces the computational complexity of previous VI algorithm by two orders, and an online EM algorithm that is scalable to extremely large tensors. To showcase the advantages of our model, we conduct extensive experiments on both simulation data and real-world applications.
Code (1)
Tasks
Variational InferenceMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Scalable Bayesian Non-Negative Tensor Factorization for Massive Count Data
We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can han…
Tensor Decompositions: A New Concept in Brain Data Analysis?
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component …
blind source separationClassificationClusteringDimensionality Reduction+2Bayesian Poisson-Randomized Gamma Tensor Factorization with Application to International Trade Flows
We study sparse semi-continuous tensor data with excess zeros, heavy right tails, and slice-specific dispersion. Such features arise naturally in monetary-valued multi-way data, such as international trade, where most ex…
Projected Tensor-Tensor Products for Efficient Computation of Optimal Multiway Data Representations
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained f…
Bayesian Robust Tensor Factorization for Incomplete Multiway Data
We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and…
Model SelectionVariational Inference