Automatic Debiased Machine Learning via Riesz Regression

Abstract: A variety of interesting parameters may depend on high dimensional regressions. Machine learning can be used to estimate such parameters. However estimators based on machine learners can be severely biased by regularization and/or model selection. Debiased machine learning uses Neyman orthogonal estimating equations to reduce such biases. Debiased machine learning generally requires estimation of unknown Riesz representers. A primary innovation of this paper is to provide Riesz regression estimators of Riesz representers that depend on the parameter of interest, rather than explicit formulae, and that can employ any machine learner, including neural nets and random forests. End-to-end algorithms emerge where the researcher chooses the parameter of interest and the machine learner and the debiasing follows automatically. Another innovation here is debiased machine learners of parameters depending on generalized regressions, including high-dimensional generalized linear models. An empirical example of automatic debiased machine learning using neural nets is given. We find in Monte Carlo examples that automatic debiasing sometimes performs better than debiasing via inverse propensity scores and never worse. Finite sample mean square error bounds for Riesz regression estimators and asymptotic theory are also given.