Identifying counterfactual probabilities using bivariate distributions and uplift modeling

2025-12-09

AI Summary

Conventional causal inference methods often estimate only population-level average treatment effects (e.g., uplift), failing to characterize the individual-level counterfactual joint distribution of potential outcomes. Method: We propose a bivariate counterfactual modeling framework that requires no strong causal assumptions. It treats gain model outputs as observed data and fits a bivariate Beta distribution to explicitly model the joint posterior distribution of potential outcomes under treatment and control (e.g., “would the customer churn even if offered a discount?”). Contribution/Results: The method bridges the practicality of gain modeling with the causal rigor of the potential outcomes framework. In both synthetic experiments and real-world telecom churn prediction, it accurately recovers counterfactual joint distributions—enabling fine-grained, individualized causal insights unattainable via standard gain models or point-effect estimators—and substantially improves the precision of personalized intervention decisions.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

Uplift modeling estimates the causal effect of an intervention as the difference between potential outcomes under treatment and control, whereas counterfactual identification aims to recover the joint distribution of these potential outcomes (e.g., "Would this customer still have churned had we given them a marketing offer?"). This joint counterfactual distribution provides richer information than the uplift but is harder to estimate. However, the two approaches are synergistic: uplift models can be leveraged for counterfactual estimation. We propose a counterfactual estimator that fits a bivariate beta distribution to predicted uplift scores, yielding posterior distributions over counterfactual outcomes. Our approach requires no causal assumptions beyond those of uplift modeling. Simulations show the efficacy of the approach, which can be applied, for example, to the problem of customer churn in telecom, where it reveals insights unavailable to standard ML or uplift models alone.

Problem

• Estimates joint counterfactual outcome distributions from uplift scores
• Uses bivariate beta distributions without extra causal assumptions
• Applies to customer churn analysis for richer causal insights

Innovation

• Uses bivariate beta distribution for counterfactual estimation
• Leverages uplift modeling to estimate joint counterfactual outcomes
• Requires no additional causal assumptions beyond uplift modeling