Yiyi Huo, Yingying Fan, Fang Han
arXiv 28 Nov 2023 · Mathematics — Statistics Theory
arXiv:2311.16486 · PDF · DOI · OpenAlex · Extracted main text
Researchers often hold the belief that random forests are "the cure to the world's ills" (Bickel, 2010). But how exactly do they achieve this? Focused on the recently introduced causal forests (Athey and Imbens, 2016; Wager and Athey, 2018), this manuscript aims to contribute to an ongoing research trend towards answering this question, proving that causal forests can adapt to the unknown covariate manifold structure. In particular, our analysis shows that a causal forest estimator can achieve the optimal rate of convergence for estimating the conditional average treatment effect, with the covariate dimension automatically replaced by the manifold dimension. These findings align with analogous observations in the realm of deep learning and resonate with the insights presented in Peter Bickel's 2004 Rietz lecture.
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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 | Wager, S. and Athey, S (2018) Estimation and inference of heterogeneous treatment effects using random forests | 1.000 | 9 | 4 | 100% |
| 2 | Athey, S. and Imbens, G (2016) Recursive partitioning for heterogeneous causal effects | 1.000 | 6 | 3 | 100% |
| 3 | Lin, Z. and Han, F (2022) On regression-adjusted imputation estimators of the average treatment effect self | 0.959 | 17 | 6 | 88% |
| 4 | Biau, G (2012) Analysis of a random forests model | 0.737 | 3 | 2 | 100% |
| 5 | Biau, G., Devroye, L., and Lugosi, G (2008) Consistency of random forests and other averaging classifiers | 0.644 | 2 | 2 | 100% |
| 6 | Biau, G. and Scornet, E (2016) A random forest guided tour | 0.644 | 2 | 2 | 100% |
| 7 | Breiman, L (2001) Random forests | 0.644 | 2 | 2 | 100% |
| 8 | Chi, C.-M., Vossler, P., Fan, Y., and Lv, J (2022) Asymptotic properties of high-dimensional random forests self | 0.644 | 2 | 2 | 100% |
| 9 | Imbens, G. W. and Rubin, D. B (2015) Causal Inference in Statistics, Social, and Biomedical Sciences | 0.644 | 2 | 2 | 100% |
| 10 | Jiao, Y., Shen, G., Lin, Y., and Huang, J (2023) Deep nonparametric regression on approximate manifolds: Nonasymptotic error bounds with polynomial prefactors | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 64 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Simultaneous Inference for Local Structural Parameters with Random Forests$^*$ | 0.737 | 3 | 2 |
| 2 | On the limiting variance of matching estimators | 0.405 | 1 | 1 |