Causal Modeling with Stationary Diffusions

Lars Lorch, Andreas Krause, Bernhard Schölkopf

Keywords: causal models, SDEs, diffusions, dynamical systems, differential equations, kernels

TL;DR: We propose a new approach for modeling causality and interventional distributions using stationary SDEs.

Abstract: We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.

Submission Number: 59