Truncated Neural Likelihood Estimation for Simulation-Based Inference in State-Space Models

2026-05-20

AI Summary

State space models often pose significant challenges for parameter inference due to intractable likelihood functions. This work proposes Truncated Neural Likelihood Estimation (T-SNL), a novel approach that introduces a sequence truncation strategy to dramatically enhance training stability and computational efficiency while preserving estimation accuracy. By integrating simulation-based inference with Bayesian parameter learning, T-SNL enables amortized inference for long-sequence modeling and observation updates. Empirical evaluations demonstrate that T-SNL consistently outperforms existing methods in terms of sample efficiency, robustness, and scalability to long sequences, offering a flexible and efficient framework for parameter inference in complex dynamical systems.

Abstract

State-space models (SSMs) are powerful probabilistic tools for modeling time-varying systems with latent dynamics. Inference in SSMs involves the estimation of latent states and parameters. In this work, we focus on parameter inference, which for SSMs is in general a very challenging problem due to the intractability of the likelihood. Recently, neural estimation methods, such as sequential neural likelihood (SNL), have shown promising results in Bayesian inference problems. In this paper, we show that SNL, when applied to the SSM setting, suffers important limitations, such as requiring a large amount of simulated samples to achieve a moderate performance, scaling poorly with sequence length, while not being amortized. We then introduce a novel inference algorithm called truncated-SNL (T-SNL), which addresses the limitations of SNL. Our algorithm is more accurate, more stable and robust during training, more scalable to longer temporal sequences, and can be amortized when new observations become available. Our experiments show that T-SNL is sample-efficient, robust, and flexible algorithm which outperforms other approaches.

Problem

• state-space models
• parameter inference
• intractable likelihood
• simulation-based inference
• neural likelihood estimation

Innovation

• Truncated-SNL
• simulation-based inference
• state-space models
• neural likelihood estimation
• amortized inference