We study the problem of estimating E(g(X)), where g is a real-valued function of d variables and X is a d-dimensional Gaussian vector with a given covariance matrix. We present a new unbiased estimator for E(g(X)) that combines the randomized dimension reduction technique with principal components analysis. Under suitable conditions, we prove that our algorithm outperforms the standard Monte Carlo method by a factor of order d.
翻译:我们研究了评估E(g(X))的问题,其中g是d个变量的实值函数,X是具有给定协方差矩阵的d维高斯向量。我们提出了一种新的无偏估计器,它将随机降维技术与主成分分析相结合。在适当的条件下,我们证明了我们的算法比标准的Monte Carlo方法更优,比例为d的数量级。