# Sample-efficient neural likelihood-free Bayesian inference of implicit HMMs

arXiv: https://arxiv.org/abs/2405.01737 · HTML: https://mlsanity.com/paper/2405.01737/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 57 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 16 of 16)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [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)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Sequential Neural Methods for Likelihood-free Inference](https://mlsanity.com/paper/1811.08723/) (2018)
- [Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models](https://mlsanity.com/paper/1604.07949/) (2016)
- [Neural Superstatistics for Bayesian Estimation of Dynamic Cognitive Models](https://mlsanity.com/paper/2211.13165/) (2022)
- [The Neural Moving Average Model for Scalable Variational Inference of State Space Models](https://mlsanity.com/paper/1910.00879/) (2019)

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

- [Latent Variable Sequence Identification for Cognitive Models with Neural Network Estimators](https://mlsanity.com/paper/2406.14742/) (2024)

## Abstract (arXiv)

Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable model, such as a Hidden Markov model (HMM), these methods are designed to only estimate the parameters, rather than the joint distribution of the parameters and the hidden states. Naive application of these methods to a HMM, ignoring the inference of this joint posterior distribution, will thus produce an inaccurate estimate of the posterior predictive distribution, in turn hampering the assessment of goodness-of-fit. To rectify this problem, we propose a novel, sample-efficient likelihood-free method for estimating the high-dimensional hidden states of an implicit HMM. Our approach relies on learning directly the intractable posterior distribution of the hidden states, using an autoregressive-flow, by exploiting the Markov property. Upon evaluating our approach on some implicit HMMs, we found that the quality of the estimates retrieved using our method is comparable to what can be achieved using a much more computationally expensive SMC algorithm.