Khashayar Khosravi, Greg Lewis, Vasilis Syrgkanis
arXiv 11 Jan 2019 · Machine Learning · 4 citations (OpenAlex)
arXiv:1901.03719 · PDF · DOI · OpenAlex · Extracted main text
We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension $D$ of the conditioning variable is larger than the sample size $n$, estimation and inference is feasible as long as the distribution of the conditioning variable has small intrinsic dimension $d$, as measured by locally low doubling measures. Our estimation is based on a sub-sampled ensemble of the $k$-nearest neighbors ($k$-NN) $Z$-estimator. We show that if the intrinsic dimension of the covariate distribution is equal to $d$, then the finite sample estimation error of our estimator is of order $n^{-1/(d+2)}$ and our estimate is $n^{1/(d+2)}$-asymptotically normal, irrespective of $D$. The sub-sampling size required for achieving these results depends on the unknown intrinsic dimension $d$. We propose an adaptive data-driven approach for choosing this parameter and prove that it achieves the desired rates. We discuss extensions and applications to heterogeneous treatment effect estimation.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Susan Athey, Julie Tibshirani, and Stefan Wager (2019) Generalized random forests | 1.000 | 16 | 4 | 100% |
| 2 | Stefan Wager and Susan Athey (2018) Estimation and inference of heterogeneous treatment effects using random forests | 1.000 | 13 | 6 | 100% |
| 3 | Yingying Fan, Jinchi Lv, and Jingbo Wang (2018) Dnn: A two-scale distributional tale of heterogeneous treatment effect inference | 1.000 | 12 | 4 | 100% |
| 4 | Miruna Oprescu, Vasilis Syrgkanis, and Zhiwei Steven Wu (2018) Orthogonal random forest for heterogeneous treatment effect estimation self | 1.000 | 10 | 5 | 100% |
| 5 | Samory Kpotufe (2011) $k$-nn regression adapts to local intrinsic dimension | 1.000 | 9 | 5 | 100% |
| 6 | Sanjoy Dasgupta and Yoav Freund (2008) Random projection trees and low dimensional manifolds | 1.000 | 5 | 3 | 100% |
| 7 | Samory Kpotufe and Sanjoy Dasgupta (2012) A tree-based regressor that adapts to intrinsic dimension | 0.874 | 5 | 2 | 100% |
| 8 | Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters | 0.811 | 4 | 2 | 100% |
| 9 | Samory Kpotufe and Vikas Garg (2013) Adaptivity to local smoothness and dimension in kernel regression | 0.811 | 4 | 2 | 100% |
| 10 | Susan Athey and Guido Imbens (2016) Recursive partitioning for heterogeneous causal effects | 0.644 | 2 | 2 | 100% |
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