High-dimensional interactions detection with sparse principal hessian matrix

Cheng Yong Tang, Ethan X. Fang, Yuexiao Dong

Research output: Contribution to journalArticlepeer-review


In statistical learning framework with regressions, interactions are the contri- butions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to combina- torial complexity and limited data information. We consider detecting interactions by exploring their connections with the principal Hessian matrix. Specifically, we propose a one-step synthetic approach for estimating the principal Hessian ma- trix by a penalized M-estimator. An alternating direction method of multipliers (ADMM) is proposed to efficiently solve the encountered regularized optimization problem. Based on the sparse estimator, we detect the interactions by identifying its nonzero components. Our method directly targets at the interactions, and it requires no structural assumption on the hierarchy of the interactions effects. We show that our estimator is theoretically valid, computationally efficient, and practically useful for detecting the interactions in a broad spectrum of scenarios.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Jan 23 2019


  • ADMM
  • Interaction detection
  • Principal Hessian matrix
  • Sparse M-estimator

ASJC Scopus subject areas

  • General

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