Doubly Robust Proximal Causal Learning for Continuous Treatments
Yong Wu, Yanwei Fu, Shouyan Wang, Xinwei Sun
TL;DR
This paper introduces a kernel-based doubly robust estimator for continuous treatments in causal inference, overcoming previous limitations of binary-only models and enabling effective estimation with unmeasured confounders.
Contribution
It develops a novel kernel-based DR estimator for continuous treatments, providing theoretical guarantees and practical algorithms for nuisance function estimation.
Findings
The estimator is consistent and asymptotically normal.
It performs well on synthetic and real-world datasets.
The method reduces computational complexity in nuisance estimation.
Abstract
Proximal causal learning is a promising framework for identifying the causal effect under the existence of unmeasured confounders. Within this framework, the doubly robust (DR) estimator was derived and has shown its effectiveness in estimation, especially when the model assumption is violated. However, the current form of the DR estimator is restricted to binary treatments, while the treatment can be continuous in many real-world applications. The primary obstacle to continuous treatments resides in the delta function present in the original DR estimator, making it infeasible in causal effect estimation and introducing a heavy computational burden in nuisance function estimation. To address these challenges, we propose a kernel-based DR estimator that can well handle continuous treatments. Equipped with its smoothness, we show that its oracle form is a consistent approximation of the…
Peer Reviews
Decision·ICLR 2024 poster
Clear writing & solid theoretical results
The reviewer is not an expert in deep learning for causal inference but would assume there are working targeting the studies setting: causal effect estimation for continuous treatment under potential missing confounders. The reviewer understands the page limitation and would recommend a detailed comparison to existing literature in the appendix --- how is this method novel and why this novel kernel modification is necessary to handle the pitfalls in the current literature? The reviewer would
1. This paper is technically sound and strong. 2. The experimental studies are well done. A sufficient amount of empirical evidence for the proposed method is provided.
1. I believe that the statement of Theorem 4.5 is incorrect. More precisely, the influence function of $B(a)$ does not exist, meaning that $B(a)$ is not pathwise differentiable. However, $B(a; P^{\epsilon,h_{bw}})$ is pathwise differentiable, indicating that the influence function does exist. Therefore, to accurately state this, the term "lim" should be removed and the statement should be made with "for any $h_{bw} > 0$". 2. A practical guide is needed to solve the optimization problem in Equati
* The paper is well-structured and flows naturally. * This paper proposes an intriguing research topic within proximal causal inference work. * Theoretical guarantee is also provided.
* The inference issue seems to be ignored without the analysis of asymptotical distribution for causal effect. * The paper’s rationale for the calculation of the influence function appears to be lacking, as it directly selects a specific submodel. It might be more appropriate to refer to the function derived in this paper as the efficient influence function, given that the previous doubly robust estimator for binary treatment is efficient. * The empirical coverage probability is not given. MS
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Causal Inference Techniques · Statistical Methods and Bayesian Inference · Bayesian Modeling and Causal Inference