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Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators

Ryan P. Kelly, David T. Frazier, David J. Warne, Christopher C. Drovandi

TL;DR

It is demonstrated that preconditioning combined with robust NPE increases stability and improves accuracy, calibration, and posterior-predictive fit over standard baseline methods.

Abstract

Simulation-based inference (SBI) enables parameter estimation for complex stochastic models with intractable likelihoods when model simulation is feasible. Neural posterior estimation (NPE) is a popular SBI approach that often achieves accurate inference with far fewer simulations than classical approaches. But in practice, neural approaches can be unreliable for two reasons: incompatible data summaries arising from model misspecification yield unreliable posteriors due to extrapolation, and prior-predictive draws can produce extreme summaries that lead to difficulties in obtaining an accurate posterior for the observed data of interest. Existing preconditioning schemes target well-specified settings, and their behaviour under misspecification remains unexplored. We study preconditioning under misspecification and propose preconditioned robust neural posterior estimation, which computes data-dependent weights that focus training near the observed summaries and fits a robust neural posterior approximation. We also introduce a forest-proximity preconditioning approach that uses tree-based proximity scores to down-weight outlying simulations and concentrate computation around the observed dataset. Across two synthetic examples and one real example with incompatible summaries and extreme prior-predictive behaviour, we demonstrate that preconditioning combined with robust NPE increases stability and improves accuracy, calibration, and posterior-predictive fit over standard baseline methods.

Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators

TL;DR

It is demonstrated that preconditioning combined with robust NPE increases stability and improves accuracy, calibration, and posterior-predictive fit over standard baseline methods.

Abstract

Simulation-based inference (SBI) enables parameter estimation for complex stochastic models with intractable likelihoods when model simulation is feasible. Neural posterior estimation (NPE) is a popular SBI approach that often achieves accurate inference with far fewer simulations than classical approaches. But in practice, neural approaches can be unreliable for two reasons: incompatible data summaries arising from model misspecification yield unreliable posteriors due to extrapolation, and prior-predictive draws can produce extreme summaries that lead to difficulties in obtaining an accurate posterior for the observed data of interest. Existing preconditioning schemes target well-specified settings, and their behaviour under misspecification remains unexplored. We study preconditioning under misspecification and propose preconditioned robust neural posterior estimation, which computes data-dependent weights that focus training near the observed summaries and fits a robust neural posterior approximation. We also introduce a forest-proximity preconditioning approach that uses tree-based proximity scores to down-weight outlying simulations and concentrate computation around the observed dataset. Across two synthetic examples and one real example with incompatible summaries and extreme prior-predictive behaviour, we demonstrate that preconditioning combined with robust NPE increases stability and improves accuracy, calibration, and posterior-predictive fit over standard baseline methods.
Paper Structure (19 sections, 3 theorems, 59 equations, 4 figures, 3 tables, 4 algorithms)

This paper contains 19 sections, 3 theorems, 59 equations, 4 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Simulation-based Bayesian inference
  3. Approximate Bayesian computation
  4. Neural density estimation
  5. Robust inference under model misspecification
  6. Methods
  7. Problem setup and preconditioning
  8. Theoretical properties of preconditioned NPE
  9. Preconditioned robust neural posterior estimation
  10. Examples
  11. Contaminated Weibull
  12. Sparse vector autoregression
  13. Real data: BVCBM
  14. Discussion
  15. SMC ABC background
  16. ...and 4 more sections

Key Result

Lemma 1

Under Assumption 1 in Appendix app:am_gap_proof,

Figures (4)

  • Figure 1: Posterior densities for the Weibull shape $k$ using PRNPE with SMC-ABC (left) and forest-proximity (right) preconditioning. The vertical dashed line indicates the target pseudo-truth $k^{\star}$.
  • Figure 2: Posterior predictive distributions for the compatible summaries $(\bar{x}, s^2)$ in the contaminated Weibull example using PRNPE with SMC-ABC (left) and forest-proximity (right) preconditioning. Scatter points represent 2000 draws; contours indicate the 50% (solid) and 90% (dashed) highest-density regions. The red star denotes the observed summary $\bm{s}_y$.
  • Figure 3: Marginal posterior densities for the noise scale $\sigma$ in the SVAR example using PRNPE with SMC ABC (left) and forest-proximity (right) preconditioning. The vertical dashed line indicates the target pseudo-truth $\sigma^\star$.
  • Figure 4: Posterior predictive distributions for the pooled standard deviation in the SVAR example using PRNPE with SMC ABC (left) and forest-proximity (right) preconditioning. The dashed horizontal line indicates the observed summary statistic.

Theorems & Definitions (4)

  • Lemma 1: Amortisation-gap bound
  • Lemma 2: Amortisation-gap bound
  • proof
  • Corollary 3