Subgradient Regularized Multivariate Convex Regression at Scale
Name
21m1413134.pdf
Description
Published version
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867.26 KB
Format
Adobe PDF
Checksum (MD5)
02f4fd17ccf8d30d5f37e2e405ee1036
Author(s)
Chen, Wenyu
Mazumder, Rahul
Date Issued
September 2024
Journal
SIAM Journal on Optimization
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
We present new large-scale algorithms for fitting a subgradient regularized multivari-ate convex regression function to n samples in d dimensions---a key problem in shape constrainednonparametric regression with applications in statistics, engineering, and the applied sciences. Theinfinite-dimensional learning task can be expressed via a convex quadratic program (QP) with O(nd)decision variables and O(n2) constraints. While instances with n in the lower thousands can be ad-dressed with current algorithms within reasonable runtimes, solving larger problems (e.g., n \approx 104or 105) is computationally challenging. To this end, we present an active set type algorithm onthe dual QP. For computational scalability, we allow for approximate optimization of the reducedsubproblems and propose randomized augmentation rules for expanding the active set. We derivenovel computational guarantees for our algorithms. We demonstrate that our framework can approx-imately solve instances of the subgradient regularized convex regression problem with n = 105 andd = 10 within minutes and shows strong computational performance compared to earlier approaches.
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DOI of Published Version
https://doi.org/10.1137/21M1413134
