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Model Selection for Treatment Choice: Penalized Welfare Maximization

Eric Mbakop, Max Tabord-Meehan

arXiv 11 Sep 2016 · Mathematics — Statistics Theory

arXiv:1609.03167 · PDF · Extracted main text

Abstract

This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings in which the policy maker may want to select amongst a collection of constrained subset classes: examples include choosing the number of covariates over which to perform best-subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. An important consequence of our results is that we are able to formalize model-selection using a "hold-out" procedure, where the policy maker would first estimate various policies using half of the data, and then select the policy which performs the best when evaluated on the other half of the data.

Citation extraction

39
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bartlett, Peter L, Stéphane Boucheron, and Gábor Lugosi (2002) Model selection and error estimation0.9285380%
2Kitagawa, Toru and Aleksey Tetenov (2018) Who should be treated? empirical welfare maximization methods for treatment choice0.90230673%
3Györfi, L, L Devroye, and G Lugosi (1996) A probabilistic theory of pattern recognition0.8746367%
4Athey, Susan and Stefan Wager (2017) Efficient policy learning0.87452100%
5Koltchinskii, Vladimir (2001) Rademacher penalties and structural risk minimization0.73732100%
6Boucheron, Stéphane, Olivier Bousquet, and Gábor Lugosi (2005) Theory of classification: A survey of some recent advances0.64422100%
7Kallus, Nathan (2016) Learning to personalize from observational data0.64422100%
8Koltchinskii, V (2008) Oracle inequalities in empirical risk minimization and sparse recovery problems: Lecture notes. Technical report, Technical repo…0.64422100%
9Manski, Charles F (2004) Statistical treatment rules for heterogeneous populations0.64422100%
10Stoye, Jörg (2009) Minimax regret treatment choice with finite samples0.64422100%

Showing the top 10 of 47 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Data-Driven Policy Learning for Continuous Treatments1.000267
22606.016590.937175
3PAC-Bayesian Treatment Allocation Under Budget Constraints0.92843
4Semiparametric Efficiency in Policy Learning with General Treatments0.92843
5Nonparametric Uniform Inference in Binary Classification and Policy Values0.87472
6Constrained Classification and Policy Learning0.860114
7Policy Learning with New Treatments0.84333
8On the Lower Confidence Band for the Optimal Welfare in Policy Learning0.84333
9Externally Valid Policy Choice0.73732
10Debiased Machine Learning of Aggregated Intersection Bounds and Other Causal Parameters0.73732