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Cited by 655

The DOI matches its Crossref record; 60 of the 60 references it cites were found in a registry or an index.

Best subset selection via a modern optimization lens

Open access
Bertsimas, Dimitris, King, Angela, Mazumder, Rahul·2016·The Annals of Statistics
DOI 10.1214/15-aos1388
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Abstract

In the period 1991–2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MIO problems. We present a MIO approach for solving the classical best subset selection problem of choosing $k$ out of $p$ features in linear regression given $n$ observations. We develop a discrete extension of modern first-order continuous optimization methods to find high quality feasible solutions that we use as warm starts to a MIO solver that finds provably optimal solutions. The resulting algorithm (a) provides a solution with a guarantee on its suboptimality even if we terminate the algorithm early, (b) can accommodate side constraints on the coefficients of the linear regression and (c) extends to finding best subset solutions for the least absolute deviation loss function. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with $n$ in the 1000s and $p$ in the 100s in minutes to provable optimality, and finds near optimal solutions for $n$ in the 100s and $p$ in the 1000s in minutes. We also establish via numerical experiments that the MIO approach performs better than Lasso and other popularly used sparse learning procedures, in terms of achieving sparse solutions with good predictive power.

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Metadata

Authors
Bertsimas, D., King, A., & Mazumder, R.
Venue
The Annals of Statistics
Publisher
Institute of Mathematical Statistics
Published
2016-04-01
Volume
44
Issue
2
Pages
813-852
ISSN
0090-5364 (ISSN-L)
DOI
10.1214/15-aos1388
OpenAlex
W1936663733
Cited by
655
References
60
FWCI
44.47
Type
journal article
Language
en
Open access
green

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CoChat. (2026). Citation check: Best subset selection via a modern optimization lens. https://app.cochat.ai/papers/10.1214/15-aos1388
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Bertsimas, D., King, A., & Mazumder, R. (2016). Best subset selection via a modern optimization lens. The Annals of Statistics. https://doi.org/10.1214/15-aos1388

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