arXiv 25 Oct 2023 · Statistics — Machine Learning
arXiv:2310.16945 · PDF · DOI · OpenAlex · Extracted main text
Accurate estimation of conditional average treatment effects (CATE) is at the core of personalized decision making. While there is a plethora of models for CATE estimation, model selection is a nontrivial task, due to the fundamental problem of causal inference. Recent empirical work provides evidence in favor of proxy loss metrics with double robust properties and in favor of model ensembling. However, theoretical understanding is lacking. Direct application of prior theoretical work leads to suboptimal oracle model selection rates due to the non-convexity of the model selection problem. We provide regret rates for the major existing CATE ensembling approaches and propose a new CATE model ensembling approach based on Q-aggregation using the doubly robust loss. Our main result shows that causal Q-aggregation achieves statistically optimal oracle model selection regret rates of $\frac{\log(M)}{n}$ (with $M$ models and $n$ samples), with the addition of higher-order estimation error terms related to products of errors in the nuisance functions. Crucially, our regret rate does not require that any of the candidate CATE models be close to the truth. We validate our new method on many semi-synthetic datasets and also provide extensions of our work to CATE model selection with instrumental variables and unobserved confounding.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kennedy, E. H (2020) Towards optimal doubly robust estimation of heterogeneous causal effects | 0.928 | 5 | 3 | 80% |
| 2 | Nie, X. and Wager, S (2021) Quasi-oracle estimation of heterogeneous treatment effects | 0.855 | 8 | 3 | 62% |
| 3 | Han, K. W. and Wu, H (2022) Ensemble method for estimating individualized treatment effects | 0.843 | 4 | 3 | 75% |
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| 7 | Mahajan, D., Mitliagkas, I., Neal, B., and Syrgkanis, V (2022) Empirical analysis of model selection for heterogenous causal effect estimation self | 0.644 | 4 | 2 | 50% |
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| 10 | Word, E. et al (1990) Student/teacher achievement ratio (star) tennessee's k-3 class size study. final summary report 1985-1990 | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 46 scored citations.
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| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Reevaluating Causal Estimation Methods with Data from a Product Release | 0.405 | 1 | 1 |