Decentralized Causal Discovery using Judo Calculus

TL;DR

This paper introduces a decentralized causal discovery framework using judo calculus, formalizing context-dependent causal claims across regimes with improved efficiency and performance demonstrated on synthetic and real-world datasets.

Contribution

It presents a novel formalization of causal discovery with judo calculus in a topos of sheaves, integrating it with existing methods and showing practical benefits.

Findings

Decentralized approach improves computational efficiency.

Enhanced causal discovery performance over classical methods.

Effective across diverse domains from biology to economics.

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.