Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the mismatch between the current proposal and a target distribution. In this work, we present an implicit adaptive importance sampling method that applies to complicated distributions which are not available in closed form. The method iteratively matches the moments of a set of Monte Carlo draws to weighted moments based on importance weights. We apply the method to Bayesian leave-one-out cross-validation and show that it performs better than many existing parametric adaptive importance sampling methods while being computationally inexpensive.

自适应重要性抽样是用于为重要性抽样找到良好建议分布的一类技术。提议分布通常是标准概率分布，其标准参数是根据当前提议与目标分布之间的不匹配进行调整的。在这项工作中，我们提出了一种隐式的自适应重要性抽样方法，该方法适用于无法以封闭形式提供的复杂分布。该方法根据重要性权重将一组蒙特卡洛绘图的矩与加权矩进行迭代匹配。我们将该方法应用于贝叶斯留一法交叉验证，并证明它比许多现有的参数自适应重要性抽样方法具有更好的性能，同时在计算上也很便宜。