Bounds on Representation-Induced Confounding Bias for Conditional Average Treatment Effect Estimation

Core Concepts

Representation learning methods for conditional average treatment effect (CATE) estimation can suffer from representation-induced confounding bias due to dimensionality reduction or other constraints on the representations, which can lead to biased CATE estimates.

Abstract

The content discusses the validity of representation learning methods for conditional average treatment effect (CATE) estimation. It first formalizes the concept of valid representations, where the CATE with respect to the covariates is equal to the CATE with respect to the representations. Two conditions for valid representations are identified: (1) no loss of information about confounders and outcome-predictive covariates, and (2) no introduction of M-bias.
The content then introduces the notion of representation-induced confounding bias (RICB), which occurs when low-dimensional (constrained) representations lose information about the observed confounders, leading to biased CATE estimates. It shows that the CATE with respect to the representations can be non-identifiable due to the RICB.
To address this issue, the content proposes a new, representation-agnostic refutation framework for estimating bounds on the RICB. The framework first estimates the sensitivity parameters of a marginal sensitivity model and the representation-conditional outcome distribution. It then computes the lower and upper bounds on the RICB, which can be used to improve the reliability of CATE estimation.
The effectiveness of the proposed refutation framework is demonstrated through experiments on several (semi-)synthetic benchmarks. The results show that the policies based on the estimated bounds on the RICB achieve lower error rates compared to the policies based on the original CATE estimates from representation learning methods.

Stats

The representation-conditional propensity score, πϕ
a(ϕ), can be bounded by the covariate-conditional propensity score, πx
a(x), using a sensitivity parameter Γ(ϕ): Γ(ϕ)−1 ≤ πϕ
0(ϕ)/πϕ
1(ϕ) / (πx
1(x)/πx
0(x)) ≤ Γ(ϕ).
The representation-conditional expected outcomes, µϕ
a(ϕ) and µϕ
a(ϕ), can be computed using the representation-conditional outcome distribution, P(Y = y | A = a, Φ(X) = ϕ), and the sensitivity parameter Γ(ϕ).

Quotes

"Low-dimensional (potentially constrained) representations can lose information about covariates, including information about ground-truth confounders. As we show later, such low-dimensional representations can thus lead to bias, because of which the validity of representation learning methods may be violated."
"To this end, we introduce the notion of representation-induced confounding bias (RICB). As a result of the RICB, the validity of representation learning for CATE estimation is typically violated, and we thus offer remedies in our paper."

Key Insights Distilled From

Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation

by Valentyn Mel... at arxiv.org 04-12-2024

https://arxiv.org/pdf/2311.11321.pdf

Deeper Inquiries

How can the proposed refutation framework be extended to handle more complex data structures, such as time-series or spatial data

The proposed refutation framework can be extended to handle more complex data structures, such as time-series or spatial data, by incorporating appropriate modeling techniques. For time-series data, the framework can leverage recurrent neural networks (RNNs) or long short-term memory (LSTM) networks to capture temporal dependencies and patterns. By feeding sequential data into the representation subnetwork, the framework can learn representations that account for the temporal dynamics of the data. Additionally, attention mechanisms can be employed to focus on relevant time steps or spatial regions, enhancing the interpretability of the learned representations.
For spatial data, convolutional neural networks (CNNs) can be utilized to extract spatial features and relationships. The representation subnetwork can be designed to capture spatial hierarchies and patterns in the data. By incorporating spatial pooling layers, the framework can aggregate information from different spatial locations and scales. Furthermore, graph neural networks (GNNs) can be employed for data with complex relational structures, such as social networks or molecular structures. GNNs can effectively model interactions between entities in the data and learn representations that encode relational information.

What are the potential limitations of the marginal sensitivity model used in the refutation framework, and how could alternative sensitivity models be incorporated

The marginal sensitivity model used in the refutation framework has certain limitations that should be considered. One limitation is the assumption of a fixed sensitivity parameter, which may not accurately capture the varying degrees of hidden confounding in different parts of the data space. To address this limitation, alternative sensitivity models could be incorporated, such as adaptive sensitivity models that dynamically adjust the sensitivity parameter based on the data distribution. These adaptive models can provide more flexibility in capturing the complex relationships between covariates and treatments.
Another limitation is the reliance on the assumption of no unobserved confounders, which may not hold in real-world scenarios. To mitigate this limitation, sensitivity models that account for unobserved confounding, such as outcome sensitivity models (OSMs) or propensity sensitivity models (MSMs), could be integrated into the framework. OSMs and MSMs can provide more robust estimates by considering the potential impact of unobserved factors on the treatment effect estimation.

Can the insights from this work on representation-induced confounding bias be applied to other causal inference tasks beyond CATE estimation, such as causal discovery or counterfactual prediction

The insights from this work on representation-induced confounding bias can be applied to other causal inference tasks beyond CATE estimation, such as causal discovery or counterfactual prediction. In causal discovery, understanding the biases introduced by representation learning methods can help in identifying spurious correlations or confounding variables that may affect causal relationships. By considering the limitations of representation-induced bias, causal discovery algorithms can be designed to account for these biases and provide more accurate causal inference.
In counterfactual prediction tasks, the insights on representation-induced confounding bias can guide the development of robust counterfactual models that account for the limitations of low-dimensional representations. By incorporating bounds on the representation-induced bias, counterfactual prediction models can provide more reliable estimates of counterfactual outcomes and treatment effects. Additionally, the framework can be extended to handle heterogeneous treatment effects and complex causal structures in counterfactual prediction tasks.