Provable sparse tensor decomposition

Will Wei Sun, Junwei Lu, Han Liu, Guang Cheng

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


We propose a novel sparse tensor decomposition method, namely the tensor truncated power method, that incorporates variable selection in the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family of high dimensional latent variable models, including high dimensional Gaussian mixtures and mixtures of sparse regressions. A thorough theoretical investigation is further conducted. In particular, we show that the final decomposition estimator is guaranteed to achieve a local statistical rate, and we further strengthen it to the global statistical rate by introducing a proper initialization procedure. In high dimensional regimes, the statistical rate obtained significantly improves those shown in the existing non-sparse decomposition methods. The empirical advantages of tensor truncated power are confirmed in extensive simulation results and two real applications of click-through rate prediction and high dimensional gene clustering.

Original languageEnglish (US)
Pages (from-to)899-916
Number of pages18
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number3
StatePublished - Jun 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Global convergence
  • Latent variable models
  • Non-convex optimization
  • Sparsity
  • Tensor decomposition


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