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Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings

Henrik Häggström, Pedro L. C. Rodrigues, Geoffroy Oudoumanessah, Florence Forbes, Umberto Picchini

TL;DR

This work proposes an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions, and produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods.

Abstract

Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI methods have made use of neural networks (NN) to provide approximate, yet expressive constructs for the unavailable likelihood function and the posterior distribution. However, the trade-off between accuracy and computational demand leaves much space for improvement. In this work, we propose an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions. Our approach produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods, even for multimodal posteriors, while exhibiting a much smaller computational footprint. We illustrate our results on several benchmark models from the SBI literature and on a biological model of the translation kinetics after mRNA transfection.

Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings

TL;DR

This work proposes an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions, and produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods.

Abstract

Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI methods have made use of neural networks (NN) to provide approximate, yet expressive constructs for the unavailable likelihood function and the posterior distribution. However, the trade-off between accuracy and computational demand leaves much space for improvement. In this work, we propose an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions. Our approach produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods, even for multimodal posteriors, while exhibiting a much smaller computational footprint. We illustrate our results on several benchmark models from the SBI literature and on a biological model of the translation kinetics after mRNA transfection.
Paper Structure (45 sections, 33 equations, 66 figures, 3 tables, 3 algorithms)

This paper contains 45 sections, 33 equations, 66 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Amortized surrogates for likelihoods and posteriors via GLLiM
  4. SeMPLE: sequential learning of likelihoods and posteriors
  5. Numerical illustrations
  6. Two Moons
  7. Multiple hyperboloid model
  8. Lotka-Volterra
  9. Biological model of the translation kinetics after mRNA transfection
  10. Resource requirement metrics
  11. Results summary
  12. Conclusion and perspectives
  13. SBIBM
  14. BIC computation for selecting $K$
  15. SNPE-A
  16. ...and 30 more sections

Figures (66)

  • Figure 1: Two Moons model: inference using datasets #1 (top), #2 (middle) and #3 (bottom) from SBIBM. Posterior samples after 4 rounds of SeMPLE (column 1), 10 rounds of SNPE-C and SNL (columns 2 and 3). All methods used a total budget of 10K model simulations. The true posteriors are in column 4.
  • Figure 2: Two Moons. (left) Median C2ST (the lower the better) and median cumulative runtime in minutes (right) for 10 runs with different data sets vs the number of model simulations. Shaded bands enclose the min and max values. C2ST is the two-samples classifier test, taking values in [0.5,1], see Section \ref{['sec:examples']}.
  • Figure 3: Hyperboloid. Median C2ST (left) and median cumulative runtime in minutes (right) for 10 runs with the same data vs the number of model simulations. Shaded bands enclose the min and max values.
  • Figure 4: Hyperboloid. An example of marginal posteriors and samples from the last round of each algorithm. The SNL marginal posteriors are not reported as their inference is completely off.
  • Figure 5: Lotka-Volterra. Marginal posteriors from SMC-ABC and SeMPLE. SeMPLE is run for a total of 30,000 model simulations. We report posterior samples from blockedopt SMC-ABC after a total of 32,865 and 3,337,640 model simulations. We also report the posterior samples from standard SMC-ABC after a total of 30,436 model simulations. True parameter values are indicated with black vertical lines.
  • ...and 61 more figures