Tokenised Flow Matching for Hierarchical Simulation Based Inference

TL;DR

The paper introduces TFMPE, a novel likelihood factorisation approach using tokenised flow matching for hierarchical simulation-based inference, reducing computational costs while maintaining accurate posterior estimates.

Contribution

It proposes a new method, TFMPE, that leverages likelihood factorisation and tokenised flow matching to improve efficiency in hierarchical SBI.

Findings

TFMPE achieves well-calibrated posteriors on benchmarks and real-world models.

The approach reduces simulation costs compared to existing hierarchical SBI methods.

A new benchmark for hierarchical SBI is introduced for systematic evaluation.

Abstract

The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchical SBI approaches factorise the posterior yet still simulate across multiple sites per training sample; We instead explore likelihood factorisation (LF) to train from single-site simulations. In LF sampling we learn a per-site neural surrogate of the simulator and then assemble synthetic multi-site observations to amortise inference for the full hierarchical posterior. Building on this, we propose Tokenised Flow Matching for Posterior Estimation (TFMPE), a tokenised flow matching approach that supports function-valued observations through likelihood factorisation. To enable systematic evaluation, we introduce a benchmark for hierarchical SBI. We validate TFMPE on this benchmark and on realistic infectious disease and computational fluid dynamics models, finding well-calibrated posteriors while reducing computational cost.