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2017

Orthogonal Machine Learning: Power and Limitations

Mackey, Lester, Syrgkanis, Vasilis, Zadik, Ilias

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Double machine learning provides $\sqrt{n}$-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an $n^{-1/4}$ rate.

The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance parameters.
We show that the $n^{-1/4}$ requirement can be improved to $n^{-1/(2k+2)}$ by employing a $k$-th order notion of orthogonality that grants robustness to more complex or higher-dimensional nuisance parameters.
In the partially linear regression setting popular in causal inference, we show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed.

Orthogonal Machine Learning: Power and Limitations · Around

Built on

Differentiation under the integral sign
Flanders, H · 1973
Earlier work this paper cites.
C(α) tests and their use
Neyman, J · 1979
Earlier work this paper cites.
Estimation of the mean of a multivariate normal distribution
Stein, C. M · 1981
Earlier work this paper cites.
Chapter 36 large sample estimation and hypothesis testing
Newey, W. and McFadden, D.l · 1994
Earlier work this paper cites.

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