Gaussian regression with convex constraints

Matey Neykov*

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


The focus of this paper is the linear model with Gaussian design under convex constraints. Specifically, we study the performance of the constrained least squares estimate. We derive two general results characterizing its performance - one requiring a tangent cone structure, and one which holds in a general setting. We use our general results to analyze three functional shape constrained problems where the signal is generated from an underlying Lipschitz, monotone or convex function. In each of the examples we show specific classes of functions which achieve fast adaptive estimation rates, and we also provide non-adaptive estimation rates which hold for any function. Our results demonstrate that the Lipschitz, monotone and convex constraints allow one to analyze regression problems even in high-dimensional settings where the dimension may scale as the square or fourth degree of the sample size respectively.

Original languageEnglish (US)
StatePublished - 2020
Event22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan
Duration: Apr 16 2019Apr 18 2019


Conference22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability


Dive into the research topics of 'Gaussian regression with convex constraints'. Together they form a unique fingerprint.

Cite this