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

2026-01-02

AI Summary

This work addresses the challenge of performing Bayesian inference with complex black-box generative models that lack tractable likelihoods and gradients. To this end, the authors propose a gradient-free ensemble-based transformed Langevin dynamics method. Their approach uniquely integrates an affine-invariant ensemble covariance structure with Maximum Mean Discrepancy (MMD) to construct a generalized Bayesian inference framework, enabling efficient posterior approximation without requiring simulator derivatives. Experimental results demonstrate that the method achieves comparable or superior accuracy to existing gradient-dependent approaches in high-dimensional and potentially misspecified settings—such as chaotic dynamical systems and scenarios with contaminated data—while substantially reducing computational cost.

Technology Category

• Machine Learning: Bayesian Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Bayesian inference
• generative models
• likelihood-free inference
• gradient-free methods
• black-box simulators

Innovation

• gradient-free
• ensemble transform
• generalized Bayesian inference
• maximum mean discrepancy
• likelihood-free inference