Sparse tensor additive regression

Botao Hao, Boxiang Wang, Pengyuan Wang, Jingfei Zhang, Jian Yang, Will Wei Sun

Research output: Contribution to journalArticlepeer-review

Abstract

Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-rank structures in the tensor additive regression. We formulate the parameter estimation as a non-convex optimization problem, and propose an efficient penalized alternating minimization algorithm. We establish a non-asymptotic error bound for the estimator obtained from each iteration of the proposed algorithm, which reveals an interplay between the optimization error and the statistical rate of convergence. We demonstrate the efficacy of STAR through extensive comparative simulation studies, and an application to the click-through-rate prediction in online advertising.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
Volume22
StatePublished - 2021

Keywords

  • Additive models
  • Low-rank tensor
  • Non-asymptotic analysis
  • Non-convex optimization
  • Tensor regression

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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