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Preconditioned Neural Posterior Estimation for Likelihood-free Inference

Xiaoyu Wang, Ryan P. Kelly, David J. Warne, Christopher Drovandi

TL;DR

This paper proposes preconditioned NPE (PNPE) and its sequential version (PSNPE), which uses a short run of ABC to effectively eliminate regions of parameter space that produce large discrepancy between simulations and data and allow the posterior emulator to be more accurately trained.

Abstract

Simulation based inference (SBI) methods enable the estimation of posterior distributions when the likelihood function is intractable, but where model simulation is feasible. Popular neural approaches to SBI are the neural posterior estimator (NPE) and its sequential version (SNPE). These methods can outperform statistical SBI approaches such as approximate Bayesian computation (ABC), particularly for relatively small numbers of model simulations. However, we show in this paper that the NPE methods are not guaranteed to be highly accurate, even on problems with low dimension. In such settings the posterior cannot be accurately trained over the prior predictive space, and even the sequential extension remains sub-optimal. To overcome this, we propose preconditioned NPE (PNPE) and its sequential version (PSNPE), which uses a short run of ABC to effectively eliminate regions of parameter space that produce large discrepancy between simulations and data and allow the posterior emulator to be more accurately trained. We present comprehensive empirical evidence that this melding of neural and statistical SBI methods improves performance over a range of examples, including a motivating example involving a complex agent-based model applied to real tumour growth data.

Preconditioned Neural Posterior Estimation for Likelihood-free Inference

TL;DR

This paper proposes preconditioned NPE (PNPE) and its sequential version (PSNPE), which uses a short run of ABC to effectively eliminate regions of parameter space that produce large discrepancy between simulations and data and allow the posterior emulator to be more accurately trained.

Abstract

Simulation based inference (SBI) methods enable the estimation of posterior distributions when the likelihood function is intractable, but where model simulation is feasible. Popular neural approaches to SBI are the neural posterior estimator (NPE) and its sequential version (SNPE). These methods can outperform statistical SBI approaches such as approximate Bayesian computation (ABC), particularly for relatively small numbers of model simulations. However, we show in this paper that the NPE methods are not guaranteed to be highly accurate, even on problems with low dimension. In such settings the posterior cannot be accurately trained over the prior predictive space, and even the sequential extension remains sub-optimal. To overcome this, we propose preconditioned NPE (PNPE) and its sequential version (PSNPE), which uses a short run of ABC to effectively eliminate regions of parameter space that produce large discrepancy between simulations and data and allow the posterior emulator to be more accurately trained. We present comprehensive empirical evidence that this melding of neural and statistical SBI methods improves performance over a range of examples, including a motivating example involving a complex agent-based model applied to real tumour growth data.
Paper Structure (18 sections, 10 equations, 11 figures, 2 algorithms)

This paper contains 18 sections, 10 equations, 11 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Simulation-based Inference
  3. Approximate Bayesian computation
  4. Neural posterior estimation
  5. Illustrative Example
  6. Method
  7. Preconditioned NPE
  8. Computational cost
  9. Illustrative Example Revisited
  10. Further Experiments
  11. High-dimensional SVAR model
  12. Biphasic Voronoi cell-based model
  13. Discussion
  14. Further background for SMC ABC
  15. Experimental Details
  16. ...and 3 more sections

Figures (11)

  • Figure 1: Comparison of marginal posterior distributions between BSL (orange), NPE (dashed pink) and SNPE (red), with black dashed lines representing the true values. The SNPE results are based on three rounds.
  • Figure 2: Comparison of posterior predictive distribution of the summary statistics of observation datasets between BSL (orange), NPE (dashed pink) and PNPE (red), with black dashed lines representing the true values. The SNPE results are based on three rounds.
  • Figure 3: Performance on SVAR model. Comparison of marginal posterior distributions between BSL (orange), SNPE (red), preconditioning step (blue dash) and PNPE (green solid), with black dashed lines representing the true values.
  • Figure 4: Performance on SVAR model. Comparison of posterior predictive distributions of the summary statistics of observation datasets between BSL (orange), SNPE (red), preconditioning step (blue dash) and PNPE (green solid), with black dashed lines representing the true values.
  • Figure 5: Performance on SVAR model with 21 parameters. Comparison of marginal posterior distributions between BSL (orange), SNPE (red) and PNPE (green), with black dashed lines representing the true values. The result of SNPE uses 2 rounds.
  • ...and 6 more figures