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2016

Best Subset Binary Prediction

Chen, Le-Yu, Lee, Sokbae

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We consider a variable selection problem for the prediction of binary outcomes.

We study the best subset selection procedure by which the covariates are chosen by maximizing Manski (1975, 1985)'s maximum score objective function subject to a constraint on the maximal number of selected variables.
We show that this procedure can be equivalently reformulated as solving a mixed integer optimization problem, which enables computation of the exact or an approximate solution with a definite approximation error bound.
In terms of theoretical results, we obtain non-asymptotic upper and lower risk bounds when the dimension of potential covariates is possibly much larger than the sample size.

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Manski, C. F
1975
Earlier work this paper cites.
Patra, R. K., E. Seijo, and
Original
1976
Earlier work this paper cites.
Johnson, D., and
1978
Earlier work this paper cites.
Manski, C. F., and
1986
Earlier work this paper cites.
Kim, J., and
1990
Earlier work this paper cites.
Horowitz, J. L
1992
Earlier work this paper cites.
Matzkin, R. L
1993
Earlier work this paper cites.
Pinkse, C
1993
Earlier work this paper cites.
Talagrand, M
1994
Earlier work this paper cites.
Charlier, E., B. Melenberg, and
1995
Earlier work this paper cites.
Natarajan, B. K
1995
Earlier work this paper cites.
Devroye, L., L. Györfi, and
1996
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Magnus, J. R., and
1999
Earlier work this paper cites.
Mammen, E., and
1999
Earlier work this paper cites.
Abrevaya, J
2000
Earlier work this paper cites.
Delgado, M. A., J. M. Rodrıguez-Poo, and
2001
Earlier work this paper cites.
Lugosi, G
2002
Earlier work this paper cites.
Manski, C. F., and
2002
Earlier work this paper cites.

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