Identification and Estimation under Multiple Versions of Treatment: Mixture-of-Experts Approach

2026-01-01

AI Summary

This study addresses the challenge of causal inference when multiple unobserved versions of a treatment violate the Stable Unit Treatment Value Assumption (SUTVA), leading to biased estimates under standard approaches. To tackle this issue, the authors introduce, for the first time, a Mixture-of-Experts framework into causal inference, integrating latent variable modeling with causal identification theory. The proposed method enables the identification and estimation of version-specific causal effects even when treatment versions are unobserved. Theoretical analysis establishes the identifiability of the approach under plausible assumptions, and extensive numerical experiments demonstrate its effectiveness and robustness in accurately estimating causal effects across a variety of data-generating settings.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

The Stable Unit Treatment Value Assumption (SUTVA) includes the condition that there are no multiple versions of treatment in causal inference. Though we could not control the implementation of treatment in observational studies, multiple versions may exist in the treatment. It has been pointed out that ignoring such multiple versions of treatment can lead to biased estimates of causal effects, but a causal inference framework that explicitly deals with the unbiased identification and estimation of version-specific causal effects has not been fully developed yet. Thus, obtaining a deeper understanding for mechanisms of the complex treatments is difficult. In this paper, we introduce the Mixture-of-Experts framework into causal inference and develop a methodology for estimating the causal effects of latent versions. This approach enables explicit estimation of version-specific causal effects even if the versions are not observed. Numerical experiments demonstrate the effectiveness of the proposed method.

Problem

• multiple versions of treatment
• causal inference
• SUTVA
• version-specific causal effects
• unobserved treatment heterogeneity

Innovation

• Mixture-of-Experts
• causal inference
• multiple versions of treatment
• latent treatment
• version-specific causal effects