Rank regularization and bayesian inference for tensor completion and extrapolation

Juan Andres Bazerque, Gonzalo Mateos, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribution, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian-and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the 'ground-truth' tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50% and 15% of missing entries respectively, resulting in recovery errors at 11 dB and 15 dB.

Original languageEnglish (US)
Article number6579771
Pages (from-to)5689-5703
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number22
StatePublished - 2013


  • Bayesian inference
  • Poisson process
  • low-rank
  • missing data
  • tensor


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