Gradient-free ensemble transform methods for generalized Bayesian inference in generative models

TL;DR

This paper introduces a gradient-free ensemble transform Langevin dynamics method for generalized Bayesian inference that is computationally efficient, affine invariant, and applicable to black-box simulators, improving accuracy and reducing costs.

Contribution

It proposes a novel gradient-free approach using ensemble transforms and maximum mean discrepancy for Bayesian inference in complex models without requiring likelihood gradients.

Findings

Achieves comparable or better accuracy than gradient-based methods.

Reduces computational cost significantly.

Demonstrates robustness to model misspecification.

Abstract

Bayesian inference in complex generative models is often obstructed by the absence of tractable likelihoods and the infeasibility of computing gradients of high-dimensional simulators. Existing likelihood-free methods for generalized Bayesian inference typically rely on gradient-based optimization or reparameterization, which can be computationally expensive and often inapplicable to black-box simulators. To overcome these limitations, we introduce a gradient-free ensemble transform Langevin dynamics method for generalized Bayesian inference using the maximum mean discrepancy. By relying on ensemble-based covariance structures rather than simulator derivatives, the proposed method enables robust posterior approximation without requiring access to gradients of the forward model, making it applicable to a broader class of likelihood-free models. The method is affine invariant, computationally efficient, and robust to model misspecification. Through numerical experiments on well-specified chaotic dynamical systems, and misspecified generative models with contaminated data, we demonstrate that the proposed method achieves comparable or improved accuracy relative to existing gradient-based methods, while substantially reducing computational cost.