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

arXiv: https://arxiv.org/abs/2605.21805 · HTML: https://mlsanity.com/paper/2605.21805/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 17 of 17)

- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [Black-Box Inference for Non-Linear Latent Force Models](https://mlsanity.com/paper/1906.09199/) (2019)
- [Adaptive Approximate Bayesian Computation Tolerance Selection](https://mlsanity.com/paper/1907.01505/) (2019)
- [ABC of the Future](https://mlsanity.com/paper/2112.12841/) (2021)
- [The Neural Moving Average Model for Scalable Variational Inference of State Space Models](https://mlsanity.com/paper/1910.00879/) (2019)
- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)
- [Likelihood-Free Inference in State-Space Models with Unknown Dynamics](https://mlsanity.com/paper/2111.01555/) (2021)

## Abstract (arXiv)

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.