Orthogonal Statistical Learning
This work addresses a foundational issue in machine learning by enabling robust statistical guarantees in settings with nuisance parameters, which is incremental as it builds on existing orthogonality concepts to provide new non-asymptotic results.
The paper tackles the problem of statistical learning with an unknown nuisance parameter by analyzing a two-stage meta-algorithm that leverages Neyman orthogonality to reduce the impact of nuisance estimation error on excess risk bounds, achieving oracle rates under certain conditions on metric entropy.
We provide non-asymptotic 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 two-stage sample splitting meta-algorithm that takes as input arbitrary estimation algorithms for the target parameter and 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 meta-algorithm 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 machine learning to give new guarantees for learning with a nuisance component. Moreover, by focusing on excess risk rather than parameter estimation, we can provide rates 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 rates of the same order as if we knew the nuisance parameter are achieved.