Causal Posterior Estimation

TL;DR

Causal Posterior Estimation (CPE) introduces a normalizing flow-based approach for Bayesian inference in simulator models with intractable likelihoods, leveraging graphical model structures for improved accuracy and efficiency.

Contribution

CPE is the first method to incorporate graphical model dependencies directly into neural network-based posterior approximations for simulator models.

Findings

CPE achieves higher accuracy than existing methods.

The continuous NF architecture enables constant-time sampling.

CPE outperforms or matches state-of-the-art in experiments.

Abstract

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can simulate model outputs given parameter values. CPE utilizes a normalizing flow-based (NF) approximation to the posterior distribution which carefully incorporates the conditional dependence structure induced by the graphical representation of the model into the neural network. Thereby it is possible to improve the accuracy of the approximation. We introduce both discrete and continuous NF architectures for CPE and propose a constant-time sampling procedure for the continuous case which reduces the computational complexity of drawing samples to O(1) as for discrete NFs. We show, through an extensive experimental evaluation, that by incorporating the conditional dependencies induced by the graphical model directly into the neural network, rather than learning them from data, CPE is able to conduct highly accurate posterior inference either outperforming or matching the state of the art in the field.