论文标题
分层稀疏的Cholesky分解，并应用于高维时空过滤
Hierarchical sparse Cholesky decomposition with applications to high-dimensional spatio-temporal filtering
论文作者
论文摘要
空间统计通常涉及协方差矩阵的Cholesky分解。为了确保对高维度的可伸缩性，最近的几个近似值假设精度矩阵的稀疏因素稀疏。我们提出了一个层次的vecchia近似，其条件独立的假设暗示着精度和协方差矩阵的cholesky因子中的稀疏性。这种非凡的特性对于对高维时空滤波的应用至关重要。我们提出了一种快速而简单的算法来计算我们的分层vecchia近似，并根据拉普拉斯近似值提供了非线性数据同化的非线性数据同化的扩展。在几个数值比较中，包括对卫星数据的过滤分析，我们的方法强烈胜过替代方法。
Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse Cholesky factor of the precision matrix. We propose a hierarchical Vecchia approximation, whose conditional-independence assumptions imply sparsity in the Cholesky factors of both the precision and the covariance matrix. This remarkable property is crucial for applications to high-dimensional spatio-temporal filtering. We present a fast and simple algorithm to compute our hierarchical Vecchia approximation, and we provide extensions to non-linear data assimilation with non-Gaussian data based on the Laplace approximation. In several numerical comparisons, including a filtering analysis of satellite data, our methods strongly outperformed alternative approaches.
