Approximate Bayesian Algorithm for Tensor Robust Principal Component Analysis

Abstract

AbstractRecently proposed Tensor Robust Principal Component Analysis (TRPCA) (Lu et al. in Tensor robust principal component analysis: exact recovery of corrupted low-rank tensors via convex optimization, 2019 [14]) aims to exactly recover the low-rank and sparse components from their sum, extending the Low-Rank Tensor Completion model of Mu et al. (Lower bounds and improved relaxations for tensor recovery, 2013 [17]). We construct a Bayesian approximate inference algorithm for TRPCA, based on regression adjustment methods suggested in the literature to correct for high-dimensional nature of the problem (Blum in J Am Stat Assoc 105(491), 2010 [3]; Blum and François in Stat Comput 20(1):63–73, 2010 [4]). Our results are compared to previous studies using variational Bayes inference for tensor completion (Hawkins and Zhang in Conference: IEEE international conference on data mining, 2018 [11]). In a short application, we study spatiotemporal traffic data imputation using nine-week spatiotemporal traffic speed data set of Guangzhou, China.KeywordsTensor robust PCALow-rankTensor completionApproximate bayesian computationRegression adjustmentVariational bayesAMS Subject Classification62F15