Compositional simulation-based inference for time series

2024-11-05

arXiv.org

AI Summary

This work addresses Bayesian inference for time-series models that are non-differentiable and lack explicit likelihoods. Conventional simulation-based inference (SBI) suffers from poor scalability in high-dimensional dynamical systems due to its reliance on massive simulations. We propose a novel Markov-structured SBI method that, for the first time, integrates local state-transition consistency estimation with weighted combinatorial inference: leveraging the simulator’s Markov property, we perform neural posterior score estimation (SNPE) and neural likelihood-ratio estimation at each time step, then fuse these local estimates into a global posterior. This design drastically reduces dependence on large-scale temporal simulations and overcomes the scalability bottleneck of amortized SBI in high-dimensional dynamics. Evaluated on ecological, epidemiological, and million-dimensional Kolmogorov flow simulation tasks, our method achieves higher posterior accuracy with fewer simulations—yielding up to several-fold improvements in simulation efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Probabilistic Inference
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Efficient Bayesian inference for time series data.
• Reducing simulation requirements in amortized SBI methods.
• Scalable parameter estimation for high-dimensional scientific simulators.

Innovation

• Amortized SBI with neural networks for Bayesian inference
• Local parameter identification using Markovian simulators
• Composition of local results for global posterior estimation