# Likelihood-Free Inference in State-Space Models with Unknown Dynamics

arXiv: https://arxiv.org/abs/2111.01555 · HTML: https://mlsanity.com/paper/2111.01555/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 121 references that are in the map.
- First posted on arXiv 2 Nov 2021.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [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)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models](https://mlsanity.com/paper/1501.03291/) (2015)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Learning to Predict the Cosmological Structure Formation](https://mlsanity.com/paper/1811.06533/) (2018)
- [Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models](https://mlsanity.com/paper/1906.05828/) (2019)
- [ELFI: Engine for Likelihood-Free Inference](https://mlsanity.com/paper/1708.00707/) (2017)
- [Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models](https://mlsanity.com/paper/1604.07949/) (2016)
- [Likelihood-Free Inference with Deep Gaussian Processes](https://mlsanity.com/paper/2006.10571/) (2020)
- [Parameter Estimation in Hidden Markov Models with Intractable Likelihoods Using Sequential Monte Carlo](https://mlsanity.com/paper/1311.4117/) (2013)
- [Structured Variational Inference in Unstable Gaussian Process State Space Models](https://mlsanity.com/paper/1907.07035/) (2019)

## Built on by (most cited first, 1 of 1)

- [Truncated Neural Likelihood Estimation for Simulation-Based Inference in State-Space Models](https://mlsanity.com/paper/2605.21805/) (2026)

## Abstract (arXiv)

Likelihood-free inference (LFI) has been successfully applied to state-space models, where the likelihood of observations is not available but synthetic observations generated by a black-box simulator can be used for inference instead. However, much of the research up to now have been restricted to cases, in which a model of state transition dynamics can be formulated in advance and the simulation budget is unrestricted. These methods fail to address the problem of state inference when simulations are computationally expensive and the Markovian state transition dynamics are undefined. The approach proposed in this manuscript enables LFI of states with a limited number of simulations by estimating the transition dynamics, and using state predictions as proposals for simulations. In the experiments with non-stationary user models, the proposed method demonstrates significant improvement in accuracy for both state inference and prediction, where a multi-output Gaussian process is used for LFI of states, and a Bayesian Neural Network as a surrogate model of transition dynamics.