High-Dimensional Simulation-Based Inference in Latent Spaces

2026-09-29

AI Summary

This study addresses the challenge of balancing computational efficiency and accuracy in simulation-based inference (SBI) within high-dimensional parameter spaces by proposing a novel framework that integrates SBI with latent generative models. The core innovation lies in compressing the inference target itself for the first time, performing posterior inference in a low-dimensional latent space before mapping it back to the original space. Furthermore, this work establishes the theoretical conditions and trade-off mechanisms governing posterior recovery in the latent space. Experimental results demonstrate that, under matched computational budgets, the proposed method maintains accuracy and calibration comparable to baselines while achieving over an order-of-magnitude improvement in sampling speed, thereby substantially optimizing high-dimensional Bayesian inference workflows.

Abstract

Neural simulation-based inference (SBI) has been widely successful in inferring a relatively small number of interpretable parameters from potentially high-dimensional observations, such as images or time series. Accordingly, representation learning in SBI has focused almost exclusively on compressing the observations used to condition the posterior. More recently, however, SBI has begun to target increasingly high-dimensional parameter spaces, raising the complementary question of whether the inference target itself should be compressed. Our answer is a practical merger of SBI and latent generative modeling, which learns a low-dimensional representation of the simulator parameters, performs posterior inference directly in this latent space, and maps posterior samples back to the original parameter space. We characterize the conditions under which latent-space inference recovers the desired target posterior and systematically study its empirical trade-offs. Across four case studies and three generative families, we compare latent and standard estimators while controlling for network capacity, regularization, optimization, and training compute. At matched training compute, latent-space inference achieves accuracy and marginal calibration comparable to direct target-space inference while sampling up to more than an order of magnitude faster.

Problem

• Simulation-Based Inference
• High-Dimensional Parameter Space
• Latent Space
• Representation Learning

Innovation

• Simulation-Based Inference
• Latent Generative Modeling
• High-Dimensional Parameters
• Representation Learning
• Posterior Inference