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：重要性采样是校正许多统计与机器学习问题中分布失配的强大工具，但在实践中其性能受限于使用重要性权重可解析计算的简单提议分布。为克服这一局限，Liu与Lee（2017）提出了一种黑箱重要性采样（BBIS）算法，该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，这需要掌握目标分布的得分函数，而对许多贝叶斯问题而言该函数难以计算。为此，本文提出另一种基于最小能量设计的新型BBIS算法——BBIS-MED，该方法仅需非归一化密度函数即可运行，可作为后处理步骤提升马尔可夫链蒙特卡洛样本质量。通过广泛模拟实验及一个得分函数无法解析推导的真实世界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。