2023/10/12 by Chaofan Huang, V. Roshan Joseph, Huang, Chaofan +1
Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2310.07953
openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.