Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-$m$ rate, where $m$ is the number of simulated samples. This can lead to significant computational challenges since a large $m$ is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

翻译：无似然推断方法通常依赖于模拟数据与真实数据之间的距离度量。一个典型例子是最大均值差异（MMD），该方法先前已被应用于近似贝叶斯计算、最小距离估计、广义贝叶斯推断以及非参数学习框架中。MMD通常以根$m$速率进行估计，其中$m$为模拟样本数量。由于需要大量$m$才能获得精确估计（这对参数估计至关重要），这一过程往往带来显著的计算挑战。本文提出一种具有显著改进样本复杂度的新型MMD估计器。该估计器特别适用于计算成本高昂但输入维度为低至中维度的平滑模拟器。这一结论通过理论结果及基于基准模拟器的大量仿真研究均得到验证。