Importance sampling is a powerful tool for correcting the distributional mismatch in many statistical and machine learning problems, but in practice its performance is limited by the usage of simple proposals whose importance weights can be computed analytically. To address this limitation, Liu and Lee (2017) proposed a Black-Box Importance Sampling (BBIS) algorithm that computes the importance weights for arbitrary simulated samples by minimizing the kernelized Stein discrepancy. However, this requires knowing the score function of the target distribution, which is not easy to compute for many Bayesian problems. Hence, in this paper we propose another novel BBIS algorithm using minimum energy design, BBIS-MED, that requires only the unnormalized density function, which can be utilized as a post-processing step to improve the quality of Markov Chain Monte Carlo samples. We demonstrate the effectiveness and wide applicability of our proposed BBIS-MED algorithm on extensive simulations and a real-world Bayesian model calibration problem where the score function cannot be derived analytically.

翻译：重要性采样是纠正许多统计与机器学习问题中分布不匹配的强大工具，但在实践中其性能受限于可解析计算重要性权重的简单提议分布的使用。为克服此局限，Liu与Lee（2017）提出了一种黑盒重要性采样算法，通过最小化核化斯坦因散度来计算任意模拟样本的重要性权重。然而，该算法需知晓目标分布的得分函数，这在许多贝叶斯问题中难以计算。为此，本文提出另一种基于最小能量设计的BBIS算法——BBIS-MED，其仅需未归一化的密度函数，可作为后处理步骤提升马尔可夫链蒙特卡洛样本质量。通过大量模拟实验及一个得分函数无法解析推导的真实贝叶斯模型校准问题，我们验证了所提BBIS-MED算法的有效性与广泛适用性。