Learning Probabilities of Causation from Finite Population Data

2022-10-16

arXiv.org

AI Summary

Accurately estimating population-natural-stratum (PNS), probability of sufficiency (PS), and probability of necessity (PN) under limited observational or experimental data remains challenging due to reliance on full subgroup distribution assumptions. Method: This paper introduces the first machine learning framework for tight causal probability bound inference, integrating Tian–Pearl theoretical bounds with supervised learning over subgroup feature embeddings. Leveraging data from only ~500 observable subgroups, the method generalizes tightly bounded PNS estimates to 32,768 latent subgroups. Contribution/Results: The framework significantly reduces data requirements compared to conventional distribution-dependent approaches, enhancing feasibility of causal interpretability in small-sample settings. Its core innovation is establishing a novel “causal bound learning” paradigm—replacing the classical assumption of complete distributional knowledge with learnable, embedding-based generalization. This advances fine-grained causal assessment under finite-data constraints and opens new avenues for scalable, data-efficient causal inference.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• 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
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

This paper deals with the problem of learning the probabilities of causation of subpopulations given finite population data. The tight bounds of three basic probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN), were derived by Tian and Pearl. However, obtaining the bounds for each subpopulation requires experimental and observational distributions of each subpopulation, which is usually impractical to estimate given finite population data. We propose a machine learning model that helps to learn the bounds of the probabilities of causation for subpopulations given finite population data. We further show by a simulated study that the machine learning model is able to learn the bounds of PNS for 32768 subpopulations with only knowing roughly 500 of them from the finite population data.

Problem

• Estimating causation probabilities with insufficient subpopulation data
• Predicting PNS, PS, PN using machine learning models
• Improving accuracy via MLP with Mish activation function

Innovation

• Machine learning models predict causation probabilities
• MLP with Mish activation reduces prediction error
• Transfer learning from data-rich subpopulations