  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.
