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Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models

Stefania Scheurer, Philipp Reiser, Tim Brünnette, Wolfgang Nowak, Anneli Guthke, Paul-Christian Bürkner

TL;DR

The proposed Uncertainty-Aware Surrogate-based Amortized Bayesian Inference (UA-SABI) is a framework that combines surrogate modeling and ABI while explicitly quantifying and propagating surrogate uncertainties through the inference pipeline, enabling reliable, fast, and repeated Bayesian inference for computationally expensive models, even under tight time constraints.

Abstract

Bayesian inference typically relies on a large number of model evaluations to estimate posterior distributions. Established methods like Markov Chain Monte Carlo (MCMC) and Amortized Bayesian Inference (ABI) can become computationally challenging. While ABI enables fast inference after training, generating sufficient training data still requires thousands of model simulations, which is infeasible for expensive models. Surrogate models offer a solution by providing approximate simulations at a lower computational cost, allowing the generation of large data sets for training. However, the introduced approximation errors and uncertainties can lead to overconfident posterior estimates. To address this, we propose Uncertainty-Aware Surrogate-based Amortized Bayesian Inference (UA-SABI) -- a framework that combines surrogate modeling and ABI while explicitly quantifying and propagating surrogate uncertainties through the inference pipeline. Our experiments show that this approach enables reliable, fast, and repeated Bayesian inference for computationally expensive models, even under tight time constraints.

Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models

TL;DR

The proposed Uncertainty-Aware Surrogate-based Amortized Bayesian Inference (UA-SABI) is a framework that combines surrogate modeling and ABI while explicitly quantifying and propagating surrogate uncertainties through the inference pipeline, enabling reliable, fast, and repeated Bayesian inference for computationally expensive models, even under tight time constraints.

Abstract

Bayesian inference typically relies on a large number of model evaluations to estimate posterior distributions. Established methods like Markov Chain Monte Carlo (MCMC) and Amortized Bayesian Inference (ABI) can become computationally challenging. While ABI enables fast inference after training, generating sufficient training data still requires thousands of model simulations, which is infeasible for expensive models. Surrogate models offer a solution by providing approximate simulations at a lower computational cost, allowing the generation of large data sets for training. However, the introduced approximation errors and uncertainties can lead to overconfident posterior estimates. To address this, we propose Uncertainty-Aware Surrogate-based Amortized Bayesian Inference (UA-SABI) -- a framework that combines surrogate modeling and ABI while explicitly quantifying and propagating surrogate uncertainties through the inference pipeline. Our experiments show that this approach enables reliable, fast, and repeated Bayesian inference for computationally expensive models, even under tight time constraints.
Paper Structure (46 sections, 2 theorems, 17 equations, 19 figures, 1 algorithm)

This paper contains 46 sections, 2 theorems, 17 equations, 19 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Amortized Bayesian Inference (ABI)
  4. ABI Training Data Generation
  5. Neural Posterior Estimation
  6. Uncertainty-Aware Surrogate Modeling
  7. Surrogate-based ABI (SABI)
  8. Uncertainty-Aware Surrogate-based ABI (UA-SABI)
  9. Related Work
  10. Multi-Fidelity Approaches in SBI
  11. Sequential Neural Posterior Estimation (S-NPE)
  12. Gaussian Process Surrogates in SBI
  13. Structure-Aware SBI Methods
  14. Neural Likelihood Estimation
  15. Low-Budget Simulation-based Inference with Bayesian Neural Networks
  16. ...and 31 more sections

Key Result

Proposition 1

Under ABI standard conditions, and assuming an infinite number of samples used to propagate from the surrogate posterior $p(\mathbf{c}, \sigma \mid D_T)$, the posterior distribution targeted by UA-SABI converges to the E-Post posterior.

Figures (19)

  • Figure 1: Illustrative workflow of UA-SABI training and inference.
  • Figure 2: Detailed graphical overview of UA-SABI training as implemented in \ref{['alg:training']}. First phase: training of uncertainty-aware surrogate model using sparse simulation data, yielding a posterior over surrogate parameters. Second phase: ABI training using surrogate-generated data, where full surrogate uncertainty is propagated through sampled surrogate outputs.
  • Figure 3: Context of UA-SABI and its alternatives under tight computational constraints.
  • Figure 4: LogSin recovery plots (top) and ECDF difference plots (bottom) for full-budget ABI, low-budget ABI, SABI, and UA-SABI (from left to right) over 200 ground truth samples. In the ECDF difference plots, empirical ranks are shown in blue, $95\%$ confidence bands assuming calibration are shown in grey.
  • Figure 5: LogSin recovery plots (left) and ECDF difference plots (right) comparing ABI methods to corresponding MCMC methods over 200 ground truth samples. In the ECDF difference plots, empirical ranks are shown in blue, $95\%$ confidence bands assuming calibration are shown in grey.
  • ...and 14 more figures

Theorems & Definitions (3)

  • Proposition 1
  • proof
  • Corollary 1