# Neural composite likelihood estimation: simulation based inference for time series

arXiv: https://arxiv.org/abs/2609.21762 · HTML: https://mlsanity.com/paper/2609.21762/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [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)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Compositional Score Modeling for Simulation-based Inference](https://mlsanity.com/paper/2209.14249/) (2022)
- [Scalable Bayes via Barycenter in Wasserstein Space](https://mlsanity.com/paper/1508.05880/) (2015)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Partitioned Variational Inference: A unified framework encompassing federated and continual learning](https://mlsanity.com/paper/1811.11206/) (2018)
- [Diffusion posterior sampling for simulation-based inference in tall data settings](https://mlsanity.com/paper/2404.07593/) (2024)
- [Expectation propagation as a way of life: A framework for Bayesian inference on partitioned data](https://mlsanity.com/paper/1412.4869/) (2014)
- [Parallelizing MCMC via Weierstrass Sampler](https://mlsanity.com/paper/1312.4605/) (2013)
- [Compositional simulation-based inference for time series](https://mlsanity.com/paper/2411.02728/) (2024)
- [Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimation](https://mlsanity.com/paper/2308.01054/) (2023)
- [Bayesian Fusion: Scalable unification of distributed statistical analyses](https://mlsanity.com/paper/2102.02123/) (2021)
- [Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applications](https://mlsanity.com/paper/2404.10899/) (2024)
- [Scalable Bayesian inference for time series via divide-and-conquer](https://mlsanity.com/paper/2106.11043/) (2021)
- [Simulation Based Composite Likelihood](https://mlsanity.com/paper/2310.10761/) (2023)

## Abstract (arXiv)

Simulation based inference (SBI) circumvents the challenge of intractable likelihoods by using a simulator that generates data given parameter values. For instance, neural likelihood estimation (NLE) estimates the likelihood function by training a neural network to perform conditional density estimation on simulated data given corresponding parameters. However such density estimation is only feasible for relatively low dimensional data. We extend the scalability of SBI methods to a higher dimensional problem: long sequences with a complex dependency structure. We introduce Neural Composite Likelihood Estimation (NCLE). This divides the sequence into smaller, equal-sized batches. Instead of training NLE to estimate the likelihood for an entire sequence, we estimate the likelihood for each batch separately. The product of these forms an approximate composite likelihood (CL), and we perform frequentist inference using methods from the CL literature: we get a point estimate from maximising the approximate CL and obtain confidence intervals by estimating the Godambe information matrix. We demonstrate the effectiveness of NCLE with experiments on time series models.