Provable Sparse Tensor Decomposition
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 23, 2016
- Source ID
- 10.1111/rssb.12190
Entities
People
- Guang Cheng
- Han Liu
- Junwei Lu
- Will Wei Sun
Organizations
- Jerry and David's guide to the World Wide Web
- National Institutes of Health
- National Science Foundation
- Office of Naval Research
- Princeton University
- Purdue University