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：典型的例子是最大平均差异(MMD),以前曾用于近似贝叶斯计算、最低距离估计、泛泛的贝叶斯推理和在非参数学习框架内使用。MMMD通常按根-百万美元的费率估算,其中百万美元是模拟样品的数量。这可能导致重大的计算挑战,因为要获得准确的估算值,需要大笔美元,这对参数估算至关重要。在本文件中,我们提议为MMD提出一个具有显著改进的样本复杂性的新颖的估测仪。估计仪特别适合计算昂贵的光滑模拟器,具有低到中维投入。这一主张通过理论结果和对基准模拟器的广泛模拟研究得到支持。