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Provable sparse tensor decomposition

Author(s): Sun, Will Wei; Lu, Junwei; Liu, Han; Cheng, Guang

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Abstract: 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.
Publication Date: 2017
Citation: Sun, Will Wei, Junwei Lu, Han Liu, and Guang Cheng. "Provable sparse tensor decomposition." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79, no. 3 (2017): 899-916. doi:10.1111/rssb.12190
DOI: doi:10.1111/rssb.12190
ISSN: 1369-7412
EISSN: 1467-9868
Pages: 899 - 916
Type of Material: Journal Article
Journal/Proceeding Title: Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Version: Author's manuscript

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