论文标题
在具有噪声的高斯过程模型中利用筛选的可扩展方法
A Scalable Method to Exploit Screening in Gaussian Process Models with Noise
论文作者
论文摘要
一种规模上近似高斯对数类似物的常见方法，它利用了一个事实，即在某些情况下，稀疏的矩阵可以很好地对精度矩阵进行良好的影响。该策略是由\ emph {筛选效应}激励的，该策略是指在$ \ mathbf {x} _0 $的点上对过程$ z $的线性预测的现象，主要取决于最接近$ \ $ \ mathbf {x}} _0 $ $的测量值。但是简单的扰动，例如I.I.D.测量噪声可以显着降低这种可利用现象的程度。尽管解决此问题的策略已经存在，并且肯定正在改善忽略该问题，但在这项工作中，我们根据EM算法提出了一种新的算法，该算法具有多种优势。在这项工作中，我们专注于Vecchia近似的应用（1988），这是一个特别受欢迎且功能强大的框架，在该框架中，我们可以证明对M步骤进行真正的二阶优化，但该方法也可以完全使用矩阵向量产品应用，使其适用于非常宽的基于精确的基质矩阵近似方法。
A common approach to approximating Gaussian log-likelihoods at scale exploits the fact that precision matrices can be well-approximated by sparse matrices in some circumstances. This strategy is motivated by the \emph{screening effect}, which refers to the phenomenon in which the linear prediction of a process $Z$ at a point $\mathbf{x}_0$ depends primarily on measurements nearest to $\mathbf{x}_0$. But simple perturbations, such as i.i.d. measurement noise, can significantly reduce the degree to which this exploitable phenomenon occurs. While strategies to cope with this issue already exist and are certainly improvements over ignoring the problem, in this work we present a new one based on the EM algorithm that offers several advantages. While in this work we focus on the application to Vecchia's approximation (1988), a particularly popular and powerful framework in which we can demonstrate true second-order optimization of M steps, the method can also be applied using entirely matrix-vector products, making it applicable to a very wide class of precision matrix-based approximation methods.
