Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation

TL;DR

This work tackles bias in CATE estimation when representation learning compresses covariates into low-dimensional spaces, creating representation-induced confounding bias (RICB). It introduces a representation-agnostic refutation framework that uses a marginal sensitivity model to bound RICB and provide partial identification of CATE, implemented via a neural framework that integrates with existing CATE methods. The approach yields valid, sharp bounds and is shown to improve decision-making by enabling deferral of uncertain cases, reducing policy error across synthetic and real-world-like benchmarks. The proposed framework thus enhances the reliability and safety of CATE estimates derived from constrained representations in practical applications.

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, we propose a neural refutation framework which performs partial identification of CATE or, equivalently, aims at estimating lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our refutation framework is of direct relevance in practice where the validity of CATE estimation is of importance.

Figures (8)

• Figure 1: The validity of CATE estimation is influenced by the different constraints imposed on representations $\Phi(\cdot)$. In red: different violations of valid CATE estimation.
• Figure 2: Our neural refutation framework for estimating bounds on the RICB. In Stage 0, we fit some representation learning method for CATE, possibly with different constraints like balancing with an empirical probability metric and invertibility, or loss re-weighting. In Stage 1, we estimate the sensitivity parameters of the MSM, $\Gamma(\phi)$, and the representation-conditional outcome distribution, $\mathbb{P}(Y \mid A = a, \Phi(x) = \phi)$. In Stage 2, we compute the lower and upper bounds on the RICB.
• Figure 3: Parallel worlds network with observed outcome $Y$ and potential outcome $Y[a]$. In the diagram, (1) $X^\Delta$ and $X^y$ d-separate $Y[a]$ from $X^\varnothing$ and $X^a$; and (2) $X^\Delta$ and $X^y$ d-separate $Y[a]$ from $A$.
• Figure 4: Policy error rate vs. deferral rate plot for synthetic data. Reported: out-sample performance of baseline methods connected with the performance of our refutation framework; mean over 10 runs. Here, $\delta$ varies in the range $\{0.0005, 0.001, 0.005, 0.01, 0.05\}$, which corresponds to several scatter points per line.
• Figure 5: Policy error rate vs. deferral rate plot for IHDP100 dataset. Reported: out-sample performance of baseline methods connected with the performance of our refutation framework; mean over 100 train/test splits. Here, $\delta$ varies in the range $\{0.0005, 0.001, 0.005, 0.01, 0.05\}$, which corresponds to several scatter points per line.

Theorems & Definitions (9)

• Definition 1: Valid representations
• Lemma 1
• proof
• Lemma 2: Removal of noise and instruments
• proof
• Lemma 3: MSM bounds on the RICB
• proof
• Corollary 1: Validity and sharpness of bounds
• proof