We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, where evaluating the likelihood function is intractable or computationally expensive, but generating outputs given parameter values is straightforward. CPE approximates the posterior distribution using flow matching while directly incorporating the conditional dependence structure induced by the model's graphical representation into the neural network architecture. Across extensive experiments, we demonstrate that hard-coding these conditional dependencies into the network, rather than requiring them to be learned from data, enables CPE to achieve highly accurate posterior inference that matches or outperforms state-of-the-art baselines.
School of Future Technology, South China University of Technology, China · State Key Laboratory of Ocean Sensing & Ocean College, Zhejiang University, China · Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, USA
Department of Statistical Science, University College London, UK · The Alan Turing Institute, UK · Department of Computer Science, Aalto University, Finland