Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks

2025-05-04

AI Summary

This paper addresses individual treatment effect (ITE) estimation by proposing the Double-Neural-Network (Double-NN) method, which introduces the Extended Faithful Inference (EFI) framework into deep neural networks for the first time—enabling rigorous uncertainty quantification of causal effects. The method employs a dual-network parameterization that circumvents classical central limit theorem constraints on model complexity, permitting network capacity to scale as $O(n^zeta)$ ($zeta < 1$) with sample size $n$ while preserving statistical validity. We establish theoretical guarantees demonstrating substantially improved scalability and provide the first statistically grounded uncertainty quantification framework for causal inference with large-scale neural networks. Empirically, Double-NN achieves significant improvements over state-of-the-art methods—including Conformalized Quantile Regression (CQR)—across multiple ITE estimation benchmarks.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Individual treatment effect estimation has gained significant attention in recent data science literature. This work introduces the Double Neural Network (Double-NN) method to address this problem within the framework of extended fiducial inference (EFI). In the proposed method, deep neural networks are used to model the treatment and control effect functions, while an additional neural network is employed to estimate their parameters. The universal approximation capability of deep neural networks ensures the broad applicability of this method. Numerical results highlight the superior performance of the proposed Double-NN method compared to the conformal quantile regression (CQR) method in individual treatment effect estimation. From the perspective of statistical inference, this work advances the theory and methodology for statistical inference of large models. Specifically, it is theoretically proven that the proposed method permits the model size to increase with the sample size $n$ at a rate of $O(n^{zeta})$ for some $0 leq zeta<1$, while still maintaining proper quantification of uncertainty in the model parameters. This result marks a significant improvement compared to the range $0leq zeta<frac{1}{2}$ required by the classical central limit theorem. Furthermore, this work provides a rigorous framework for quantifying the uncertainty of deep neural networks under the neural scaling law, representing a substantial contribution to the statistical understanding of large-scale neural network models.

Problem

• Estimates individual treatment effects using deep neural networks
• Advances uncertainty quantification in large neural network models
• Extends fiducial inference for scalable treatment effect analysis

Innovation

• Double-NN method for treatment effect estimation
• Deep neural networks model treatment effects
• Uncertainty quantification under neural scaling law