论文标题
熵最小化的分布是最佳的最佳重要性建议
Entropy minimizing distributions are worst-case optimal importance proposals
论文作者
论文摘要
考虑了属于给定凸等级的目标概率分布的重要性采样。在先前的结果中，使用目标相对于提案分布的目标熵来量化重要性成本。使用参考度量作为成本的参考，我们在某些一般条件下证明，最坏情况最佳建议是通过将分布熵最小化相对于所考虑的凸出分布类中的参考的分布来给出的。当使用定义无原子条件度量的推送前映射定义凸类类时，后一种条件特别满足。最佳建议是Gibbsian，可以使用蒙特卡洛方法进行采样。
Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to proposal distributions. Using a reference measure as a reference for cost, we prove under some general conditions that the worst-case optimal proposal is precisely given by the distribution minimizing entropy with respect to the reference within the considered convex class of distributions. The latter conditions are in particular satisfied when the convex class is defined using a push-forward map defining atomless conditional measures. Applications in which the optimal proposal is Gibbsian and can be practically sampled using Monte Carlo methods are discussed.
