Orthogonal Statistical Learning
Abstract
We provide nonasymptotic excess risk guarantees for statistical learning in a setting where the population risk with respect to which we evaluate the target parameter depends on an unknown nuisance parameter that must be estimated from data. We analyze a twostage sample splitting metaalgorithm that takes as input two arbitrary estimation algorithms: one for the target parameter and one for the nuisance parameter. We show that if the population risk satisfies a condition called Neyman orthogonality, the impact of the nuisance estimation error on the excess risk bound achieved by the metaalgorithm is of second order. Our theorem is agnostic to the particular algorithms used for the target and nuisance and only makes an assumption on their individual performance. This enables the use of a plethora of existing results from statistical learning and machine learning to give new guarantees for learning with a nuisance component. Moreover, by focusing on excess risk rather than parameter estimation, we can give guarantees under weaker assumptions than in previous works and accommodate settings in which the target parameter belongs to a complex nonparametric class. We provide conditions on the metric entropy of the nuisance and target classes such that oracle ratesrates of the same order as if we knew the nuisance parameterare achieved. We also derive new rates for specific estimation algorithms such as variancepenalized empirical risk minimization, neural network estimation and sparse highdimensional linear model estimation. We highlight the applicability of our results in four settings of central importance: 1) heterogeneous treatment effect estimation, 2) offline policy optimization, 3) domain adaptation, and 4) learning with missing data.
 Publication:

arXiv eprints
 Pub Date:
 January 2019
 arXiv:
 arXiv:1901.09036
 Bibcode:
 2019arXiv190109036F
 Keywords:

 Mathematics  Statistics Theory;
 Computer Science  Machine Learning;
 Economics  Econometrics;
 Statistics  Machine Learning