MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Sparse high-dimensional regression: Exact scalable algorithms and phase transitions

Author(s)
Bertsimas, Dimitris; Van Parys, Bart
Thumbnail
DownloadSubmitted version (597.2Kb)
Open Access Policy

Open Access Policy

Creative Commons Attribution-Noncommercial-Share Alike

Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse regression problem for sample sizes n and number of regressors p in the 100,000s, that is, two orders of magnitude better than the current state of the art, in seconds. The ability to solve the problem for very high dimensions allows us to observe new phase transition phenomena. Contrary to traditional complexity theory which suggests that the difficulty of a problem increases with problem size, the sparse regression problem has the property that as the number of samples n increases the problem becomes easier in that the solution recovers 100% of the true signal, and our approach solves the problem extremely fast (in fact faster than Lasso), while for small number of samples n, our approach takes a larger amount of time to solve the problem, but importantly the optimal solution provides a statistically more relevant regressor. We argue that our exact sparse regression approach presents a superior alternative over heuristic methods available at present.
Date issued
2020
URI
https://hdl.handle.net/1721.1/133696
Department
Massachusetts Institute of Technology. Operations Research Center
Journal
The Annals of Statistics
Publisher
Institute of Mathematical Statistics

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.