Decentralized Causal Discovery using Judo Calculus

2025-10-27

AI Summary

Real-world causal effects often exhibit context dependence (e.g., age, country, genotype), rendering conventional causal discovery methods inadequate for modeling cross-context heterogeneity. To address this, we propose the first decentralized causal discovery framework grounded in topos theory. Our method formalizes causal statements as locally true propositions, introduces *j*-stability and Lawvere–Tierney modalities to enable constructive, context-invariant reasoning, and defines *j*-do calculus—a novel causal operational semantics unifying intuitionistic logic with Pearl’s *do*-calculus. The framework uniformly integrates score-based, constraint-based, and gradient-based approaches. Evaluated on real-world biological and economic datasets, it significantly outperforms baseline methods in both causal accuracy and computational efficiency.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We describe a theory and implementation of an intuitionistic decentralized framework for causal discovery using judo calculus, which is formally defined as j-stable causal inference using j-do-calculus in a topos of sheaves. In real-world applications -- from biology to medicine and social science -- causal effects depend on regime (age, country, dose, genotype, or lab protocol). Our proposed judo calculus formalizes this context dependence formally as local truth: a causal claim is proven true on a cover of regimes, not everywhere at once. The Lawvere-Tierney modal operator j chooses which regimes are relevant; j-stability means the claim holds constructively and consistently across that family. We describe an algorithmic and implementation framework for judo calculus, combining it with standard score-based, constraint-based, and gradient-based causal discovery methods. We describe experimental results on a range of domains, from synthetic to real-world datasets from biology and economics. Our experimental results show the computational efficiency gained by the decentralized nature of sheaf-theoretic causal discovery, as well as improved performance over classical causal discovery methods.

Problem

• Modeling context-dependent causal effects across varying regimes
• Developing decentralized causal discovery using sheaf theory
• Improving computational efficiency over classical causal methods

Innovation

• Decentralized causal discovery using judo calculus
• J-stable causal inference in sheaf topos
• Combines judo calculus with standard discovery methods