Provable sparse tensor decomposition

• 成果类型: Article
• 署名作者: Sun, Will Wei; Lu, Junwei; Liu, Han; Cheng, Guang
• 署名单位: Yahoo! Inc; Princeton University; Purdue University System; Purdue University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12190
• 发表日期: 2017
• 页码: 899-916
• 关键词: individual-differences; components

摘要

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.