Decentralized Causal Discovery using Judo Calculus
Sridhar Mahadevan
TL;DR
This work generalizes causal discovery by introducing judo calculus, an intuitionistic, topos-based framework that yields local, regime-specific causal truths across covers of contexts. By modeling interventions and regime variation with a Lawvere–Tierney operator j on a presheaf of local causal models, the approach certifies edges as j-stable within each cover and glues them to produce globally valid conclusions. The authors adapt popular causal discovery methods (GES, psi-FCI, DCDI) into j-stable variants and demonstrate computational efficiency from decentralized, parallelizable per-regime learning, along with improved accuracy and robustness under regime shifts across synthetic DAGs, Sachs signaling data, LINCS perturbations, and OECD PISA datasets. The methodology unifies likelihood, topology, and invariance into TCES and related TCMS/DCDI-TCM variants, enabling stable, transportable causal inferences across heterogeneous environments. The work also presents a formal adjunction between causal and statistical models, enabling functorial, consistent updates to causal structures as CI information evolves, and outlines a path toward public implementation and broader validation.
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.