STOCHASTIC APPROXIMATION OF SCORE FUNCTIONS FOR GAUSSIAN PROCESSES
STOCHASTIC APPROXIMATION OF SCORE FUNCTIONS FOR GAUSSIAN PROCESSES
复制标题
高斯过程分数函数的随机逼近
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Anitescu
中科院分区：
文献类型：
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作者：
M. Stein;Jie Chen;M. Anitescu
我们讨论了最近推出的无偏随机近似的得分方程的高斯过程的最大似然计算的统计特性。在一定的条件下，包括协方差矩阵的有界条件数，该方法实现了O（n）的存储和接近O（n）的计算eort每一步的优化，其中n是数据站点的数量。在这里，我们证明了，如果协方差矩阵的条件数是有界的，那么近似得分方程是在一个良好的意义下的近最优。因此，不仅是近似计算效率，但它也有可比的统计性质，以确切的最大似然估计。我们讨论了一个modication的随机近似，其中随机项的设计元素模仿模式从一个2 n阶乘设计。我们证明这些设计总是至少一样好的非结构化设计，我们通过模拟表明，他们可以产生一个显着的改善随机设计。我们的ndings验证了模拟数据集上的数值实验高达100万个观察。我们将这种方法应用于时空
We discuss the statistical properties of a recently introduced unbiased stochastic approximation to the score equations for maximum likelihood calculation for Gaussian processes. Under certain conditions, including bounded condition number of the covariance matrix, the approach achieves O(n) storage and nearly O(n) computational eort per optimization step, where n is the number of data sites. Here, we prove that if the condition number of the covariance matrix is bounded, then the approximate score equations are nearly optimal in a well-dened sense. Therefore not only is the approximation efcient to compute, but it also has comparable statistical properties to the exact maximum likelihood estimates. We discuss a modication of the stochastic approximation in which design elements of the stochastic terms mimic patterns from a 2 n factorial design. We prove these designs are always at least as good as the unstructured design, and we demonstrate through simulation that they can produce a substantial improvement over random designs. Our ndings are validated by numerical experiments on simulated datasets of up to 1 million observations. We apply the approach to t a space-time