Doubly Adaptive Importance Sampling
提出一种混合方法，在变分推断和重要性采样之间自适应插值，保证每次迭代的蒙特卡洛有效样本量，用于难以处理的贝叶斯后验近似。
We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow. Therefore, we propose a hybrid where, at each iteration, the Monte Carlo effective sample size can be guaranteed at a fixed computational cost by interpolating between natural-gradient variational inference and importance sampling. The amount of damping in the updates adapts to the posterior and guarantees the effective sample size. Gaussianity enables the use of Stein’s lemma to obtain gradient-based optimization in the highly damped variational inference regime and a reduction of Monte Carlo error for undamped adaptive importance sampling. The result is a generic, embarrassingly parallel and adaptive posterior approximation method. Numerical studies on simulated and real data show its competitiveness with other, less general methods. Supplementary materials for this article are available online.