Robust Covariance Adaptation in Adaptive Importance Sampling
Robust Covariance Adaptation in Adaptive Importance Sampling
复制标题
自适应重要性采样中的鲁棒协方差自适应
DOI：
10.1109/lsp.2018.2841641
复制
发表时间：
2018
影响因子：
3.9
通讯作者：
M. Bugallo
中科院分区：
文献类型：
--
作者：
Yousef El;V. Elvira;M. Bugallo
重要性抽样（IS）是一种蒙特卡罗方法，它允许使用从另一个建议分布生成的加权样本来近似目标分布。自适应重要性采样（AIS）实现了IS的迭代版本，其适应建议分布的参数以改善对目标的估计。虽然适应的位置（平均值）的建议已在很大程度上进行了研究，AIS的一个重要挑战涉及到适应的尺度参数（协方差矩阵）的困难。在权重退化的情况下，使用经验协方差来调整协方差矩阵会导致奇异矩阵，这会导致算法在后续迭代中的性能较差。在这封信中，我们提出了一个新的计划，利用IS文献的最新进展，以防止所谓的重量退化。该方法有效地调整了提案分布群体的协方差矩阵，并在高维场景中实现了显着的性能改进。我们通过计算机模拟验证了新的方法。
Importance sampling (IS) is a Monte Carlo methodology that allows for the approximation of a target distribution using weighted samples generated from another proposal distribution. Adaptive importance sampling (AIS) implements an iterative version of IS, which adapts the parameters of the proposal distribution in order to improve estimation of the target. While the adaptation of the location (mean) of the proposals has been largely studied, an important challenge of AIS relates to the difficulty of adapting the scale parameter (covariance matrix). In the case of weight degeneracy, adapting the covariance matrix using the empirical covariance results in a singular matrix, which leads to a poor performance in subsequent iterations of the algorithm. In this letter, we propose a novel scheme which exploits recent advances in the IS literature to prevent the so-called weight degeneracy. The method efficiently adapts the covariance matrix of a population of proposal distributions and achieves a significant performance improvement in high-dimensional scenarios. We validate the new method through computer simulations.