• Corpus ID: 10674153

Orthogonal Machine Learning: Power and Limitations

@inproceedings{Mackey2018OrthogonalML,
  title={Orthogonal Machine Learning: Power and Limitations},
  author={Lester W. Mackey and Vasilis Syrgkanis and Ilias Zadik},
  booktitle={ICML},
  year={2018}
}
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… 

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References

SHOWING 1-10 OF 18 REFERENCES
Debiasing the lasso: Optimal sample size for Gaussian designs
TLDR
It is proved that the debiased estimator is asymptotically Gaussian under the nearly optimal condition $s_0 = o(n/ (\log p)^2)$, and a new estimator that is minimax optimal up to a factor $1+o_n(1)$ for i.i.d. Gaussian designs.
Double machine learning for treatment and causal parameters
TLDR
The resulting method could be called a "double ML" method because it relies on estimating primary and auxiliary predictive models and achieves the fastest rates of convergence and exhibit robust good behavior with respect to a broader class of probability distributions than naive "single" ML estimators.
Confidence intervals for low dimensional parameters in high dimensional linear models
TLDR
The method proposed turns the regression data into an approximate Gaussian sequence of point estimators of individual regression coefficients, which can be used to select variables after proper thresholding, and demonstrates the accuracy of the coverage probability and other desirable properties of the confidence intervals proposed.
Statistical Learning with Sparsity: The Lasso and Generalizations
TLDR
Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data and extract useful and reproducible patterns from big datasets.
Program evaluation and causal inference with high-dimensional data
TLDR
This paper shows that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reduced form functional parameters, and provides results on honest inference for (function-valued) parameters within this general framework where any high-quality, modern machine learning methods can be used to learn the nonparametric/high-dimensional components of the model.
On asymptotically optimal confidence regions and tests for high-dimensional models
TLDR
A general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model and develops the corresponding theory which includes a careful analysis for Gaussian, sub-Gaussian and bounded correlated designs.
Exact Post-Selection Inference for Sequential Regression Procedures
ABSTRACT We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general
Valid post-selection inference
It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees
Double/Debiased/Neyman Machine Learning of Treatment Effects
TLDR
The application of a generic double/de-biased machine learning approach for obtaining valid inferential statements about focal parameters, using Neyman-orthogonal scores and cross-fitting, in settings where nuisance parameters are estimated using ML methods is illustrated.
...
...