2022-06-28-khosravi22a.md

abstract	booktitle	title	year	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
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.	First Conference on Causal Learning and Reasoning	Non-parametric Inference Adaptive to Intrinsic Dimension	2022	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	khosravi22a	0	Non-parametric Inference Adaptive to Intrinsic Dimension	373	389	373-389	373	false	Khosravi, Khashayar and Lewis, Greg and Syrgkanis, Vasilis	given family Khashayar Khosravi given family Greg Lewis given family Vasilis Syrgkanis	2022-06-28		Proceedings of the First Conference on Causal Learning and Reasoning	177	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v177/khosravi22a/khosravi22a.pdf