Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation
Valentyn Melnychuk, Dennis Frauen, Stefan Feuerriegel
TL;DR
This paper introduces a framework to estimate bounds on the bias caused by low-dimensional representations in treatment effect estimation, addressing the trade-off between variance reduction and confounder information loss.
Contribution
It provides a theoretical analysis of when CATE is non-identifiable with constrained representations and proposes a neural refutation method to estimate bounds on the bias.
Findings
Theoretical conditions for non-identifiability of CATE with low-dimensional representations.
A neural framework for partial identification of confounding bias bounds.
Experimental validation demonstrating the effectiveness of the proposed bounds.
Abstract
State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic refutation framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATE is non-identifiable given low-dimensional (constrained) representations. Second, as our remedy,…
Peer Reviews
Decision·ICLR 2024 spotlight
This paper addresses a very important, and often overlooked, aspect of representation learning for causal effect estimation. The authors do a commendable job of describing the circumstances under which we should expect to incur bias due to representation induced confounding, and clearly delineate them from existing approaches which don't suffer from the same issues. The proposed sensitivity analysis is intuitive and the authors do a nice job of describing it's integration into the neural network
The largest weakness I see is the same as what is commonly shared throughout the sensitivity analysis literature, namely that practitioners must place assumptions on the extent of confounding.
The paper is technically sound and well-organized.
It seems that the notations/symbols are not defined correctly. For example, in the section of notations, the authors claim that $\mu_a^x(x)=\mathbb{E}(Y|A=1,X=x)$, but $\mu_a^x(x)$ should be $\mathbb{E}(Y|A=a,X=x)$. In the same paragraph, the authors claim that $\mu_a^\phi(\phi)=\mathbb{E}(Y|A=1,\Phi(X)=\phi)$, but $\mu_a^\phi(\phi)$ should be $\mathbb{E}(Y|A=a,\Phi(X)=\phi)$. In addition, the authors define $\pi_a^x(x)= \mathbb{P}(A=a|X=x)$. I wonder why the authors do not simply $\pi_a^x$ or $
- The paper presents a problem that is novel and related to the representation of learning for CATE, which is a prominent research direction. - A detailed analysis of representation-induced bias is provided. - Both real-world and synthetic experiments are performed with the proposed framework.
- The motivation for employing CDAG is not quite clear. - No theoretical proof of the proposed bounds.
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Taxonomy
TopicsAdvanced Causal Inference Techniques · Statistical Methods and Inference · Domain Adaptation and Few-Shot Learning