Differentiable Pareto-Smoothed Weighting for High-Dimensional Heterogeneous Treatment Effect Estimation (2404.17483v5)

Abstract: There is a growing interest in estimating heterogeneous treatment effects across individuals using their high-dimensional feature attributes. Achieving high performance in such high-dimensional heterogeneous treatment effect estimation is challenging because in this setup, it is usual that some features induce sample selection bias while others do not but are predictive of potential outcomes. To avoid losing such predictive feature information, existing methods learn separate feature representations using inverse probability weighting (IPW). However, due to their numerically unstable IPW weights, these methods suffer from estimation bias under a finite sample setup. To develop a numerically robust estimator by weighted representation learning, we propose a differentiable Pareto-smoothed weighting framework that replaces extreme weight values in an end-to-end fashion. Our experimental results show that by effectively correcting the weight values, our proposed method outperforms the existing ones, including traditional weighting schemes. Our code is available at https://github.com/ychika/DPSW.

• The paper introduces a novel Pareto-smoothed weighting method that stabilizes extreme IPW values through a differentiable ranking system.
• It integrates extreme value statistics with gradient-based learning to iteratively refine propensity score estimates and improve CATE accuracy.
• Empirical tests on synthetic and semi-synthetic datasets demonstrate superior performance over traditional methods in high-dimensional settings.

A Novel Framework for Stable Estimation of Heterogeneous Treatment Effects Using Pareto-Smoothed Differentiable Weighting

Introduction and Objective

This examination explores the complexities of estimating heterogeneous treatment effects from high-dimensional observational data, where traditional methods face significant challenges due to extreme weight values in Inverse Probability Weighting (IPW). IPW techniques, pivotal for addressing sample selection biases, often suffer from estimation instability under finite samples due to propensity score errors from high-dimensional feature representation.

The paper introduces a differentiated Pareto-smoothed weighting framework designed to enhance the numerical robustness of IPW weights directly within a learning setting. This approach ingeniously incorporates extreme value statistics with differentiable programming, which could potentially revolutionize the efficiency and accuracy of treatment effect estimations in various fields from healthcare to targeted marketing.

Methodological Advancements

The proposed method integrates Pareto smoothing with a differentiable ranking system to overcome the challenge of non-differentiability in weight correction processes, which traditionally impede gradient backpropagation important for end-to-end learning in neural networks. Here are the key components and steps involved in the method:

1. Pareto-Smoothed Weight Replacement: Extreme weight values, typically problematic in traditional methods, are replaced based on the quantiles of a Generalized Pareto Distribution (GPD), calculated in a novel, differentiable fashion.
2. Differentiable Ranking System: Addressing the computational crux where ranking functions are traditionally non-differentiable, the method employs a differentiable approximation using regularized linear programming. This enhancement facilitates gradient descent algorithms crucial for learning in an end-to-end parameter update setting.
3. Iterative Training Process: The framework iteratively updates the propensity model and other model parameters (feature representations and outcome prediction models) by alternating between minimizing cross-entropy loss for propensity score estimates and a weighted loss function for treatment effect estimation, using differentiable reconstructed weights.
4. Algorithmic Implementation: The practical algorithm, designed for operational efficiency, iterates through training data to update model parameters by applying the differentiable weighting corrections, ensuring robust training convergence.

Empirical Validation

The paper evaluates the proposed framework on both synthetic and semi-synthetic datasets, fundamentally demonstrating improved performance over traditional and iteration methods, especially in high-dimensional settings:

• Semi-synthetic Data Results: Experiments using healthcare and advertising datasets show superior estimation accuracy of the conditional average treatment effects (CATE), outperforming existing weighting schemes like DRCFR under variety of metrics.
• Synthetic Data Analysis: Evaluating feature attribution across different encoders illustrates that the new method effectively learns and correctly attributes the influence of various feature sets (instrumental variables, confounders, adjustment variables), which enhances the potential outcomes estimation.

Future Implications and Theoretical Contributions

The convergence of Pareto smoothing with differentiable programming augurs well for tackling high-dimensional causal inference problems, facilitating more stable and efficient learning processes. The adaptability of the framework allows for application across various fields inundated with complex, high-dimensional data. Importantly, this research paves the way for future explorations into integrating more granular statistical measures within learning frameworks, potentially leading to more refined and scalable machine learning models for causal inference.

Conclusion

In summary, this research addresses a significant gap in the literature of heterogeneous treatment effect estimation by providing a robust, scalable, and efficient method. The differentiable Pareto-smoothed weighting framework not only stabilizes the traditional extreme values in IPW but also seamlessly integrates within an end-to-end learning architecture, showcasing promising results in both theoretical and practical implementations.