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Neural composite likelihood estimation: simulation based inference for time series

arXiv 2609.21762 ↗First posted 18 Sep 2026stat.CO stat.MLcited by 0

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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.

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References · 20

  1. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  2. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  3. 2019The frontier of simulation-based inferencecited by 490
  4. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 217
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  6. 2020Neural Approximate Sufficient Statistics for Implicit Modelscited by 72
  7. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
  8. 2022Compositional Score Modeling for Simulation-based Inferencecited by 46
  9. 2015Scalable Bayes via Barycenter in Wasserstein Spacecited by 44
  10. 2025Simulation-Based Inference: A Practical Guidecited by 30
  11. 2018Partitioned Variational Inference: A unified framework encompassing federated and continual learningcited by 29
  12. 2024Diffusion posterior sampling for simulation-based inference in tall data settingscited by 17
8 more
  1. 2014Expectation propagation as a way of life: A framework for Bayesian inference on partitioned datacited by 14
  2. 2013Parallelizing MCMC via Weierstrass Samplercited by 11
  3. 2023Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimationcited by 8
  4. 2024Compositional simulation-based inference for time seriescited by 8
  5. 2021Bayesian Fusion: Scalable unification of distributed statistical analysescited by 5
  6. 2021Scalable Bayesian inference for time series via divide-and-conquercited by 3
  7. 2024Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applicationscited by 3
  8. 2023Simulation Based Composite Likelihoodcited by 1

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