Compositional simulation-based inference for time series

TL;DR

This paper introduces a novel simulation-based inference method for time series that leverages the Markovian structure of simulators to improve efficiency and scalability, demonstrated on synthetic and high-dimensional real-world data.

Contribution

It presents a new SBI approach that exploits local transition information in Markovian simulators to efficiently infer parameters from entire time series.

Findings

More simulation-efficient than global posterior estimation.

Effective on synthetic benchmarks in ecology and epidemiology.

Scalable to high-dimensional data with around one million dimensions.

Abstract

Amortized simulation-based inference (SBI) methods train neural networks on simulated data to perform Bayesian inference. While this strategy avoids the need for tractable likelihoods, it often requires a large number of simulations and has been challenging to scale to time series data. Scientific simulators frequently emulate real-world dynamics through thousands of single-state transitions over time. We propose an SBI approach that can exploit such Markovian simulators by locally identifying parameters consistent with individual state transitions. We then compose these local results to obtain a posterior over parameters that align with the entire time series observation. We focus on applying this approach to neural posterior score estimation but also show how it can be applied, e.g., to neural likelihood (ratio) estimation. We demonstrate that our approach is more simulation-efficient than directly estimating the global posterior on several synthetic benchmark tasks and simulators used in ecology and epidemiology. Finally, we validate scalability and simulation efficiency of our approach by applying it to a high-dimensional Kolmogorov flow simulator with around one million data dimensions.