Random Projection Estimation of Discrete-Choice Models with Large Choice Sets

34 Pages Posted: 17 Mar 2016 Last revised: 11 Aug 2017

See all articles by Khai Chiong

Khai Chiong

University of Texas at Dallas - Naveen Jindal School of Management

Matthew Shum

California Institute of Technology

Multiple version iconThere are 2 versions of this paper

Date Written: May 26, 2016

Abstract

We introduce sparse random projection, an important tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. First, the high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. In the second step, estimation proceeds using the cyclic monotonicity inequalities implied by the multinomial choice model; the estimation procedure is semi-parametric and does not require explicit distributional assumptions to be made regarding the random utility errors. The random projection procedure is justified via the Johnson-Lindenstrauss Lemma: – the pairwise distances between data points are preserved during data compression, which we exploit to show convergence of our estimator. The estimator works well in computational simulation and in a application to a real-world supermarket scanner dataset.

Keywords: semiparametric multinomial choice models, random projection, large choice sets, cyclic monotonicity, Johnson-Lindenstrauss Lemma

Suggested Citation

Chiong, Khai and Shum, Matthew, Random Projection Estimation of Discrete-Choice Models with Large Choice Sets (May 26, 2016). Available at SSRN: https://ssrn.com/abstract=2748700 or http://dx.doi.org/10.2139/ssrn.2748700

Khai Chiong

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Matthew Shum (Contact Author)

California Institute of Technology ( email )

Pasadena, CA 91125
United States

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