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.

翻译：复杂生成模型中的贝叶斯推断常因缺乏易处理的似然函数以及高维模拟器梯度计算的不可行性而受阻。现有的广义贝叶斯推断无似然方法通常依赖于基于梯度的优化或重参数化技术，这些方法计算成本高昂且往往不适用于黑箱模拟器。为突破这些限制，我们提出一种基于最大均值差异的梯度自由集成变换朗之万动力学方法，用于实现广义贝叶斯推断。该方法通过依赖集成协方差结构而非模拟器导数，能够在无需前向模型梯度信息的情况下实现稳健的后验分布逼近，从而适用于更广泛的无似然模型类别。该方法具有仿射不变性、计算高效性以及对模型设定错误的鲁棒性。通过对设定正确的混沌动力系统与存在数据污染的设定错误生成模型进行数值实验，我们证明所提方法在显著降低计算成本的同时，能够达到与现有基于梯度方法相当或更优的精度。