论文标题
GraphSpme：Markov Precision矩阵估计和渐近Stein型收缩
GraphSPME: Markov Precision Matrix Estimation and Asymptotic Stein-Type Shrinkage
论文作者
论文摘要
GraphSpme是一种开源Python，R和C ++ header包装封装，实现非参数稀疏精度矩阵估计以及协方差矩阵的渐近Stein型缩小估计。用户定义了潜在的邻域结构，并提供了潜在的p >> n的数据。本文介绍了一种新的方法，用于查找潜在的马尔可夫属性的最佳顺序（数据允许估计）。该算法在软件包中实现，从而减轻了用户进行马尔可夫假设并实施相应的复杂高阶邻里结构的问题。通过同时利用Markov性质和Stein型收缩来使估计准确稳定。 Stein型收缩的渐近结果可确保以自动方式获得非细井条件的矩阵。最终对称转换会产生对称的正定估计值。此外，通过利用马尔可夫假设下的精密矩阵的稀疏性质，使估计程序有效且可扩展到非常高维问题（〜10^7）。明智的是实施，通过采用特征C ++线性 - 代数库提供的稀疏可能性来利用稀疏性。包装和示例可在https://github.com/equinor/graphspme上找到
GraphSPME is an open source Python, R and C++ header-only package implement-ing non-parametric sparse precision matrix estimation along with asymptotic Stein-type shrinkage estimation of the covariance matrix. The user defines a potential neighbourhood structure and provides data that potentially are p >> n. This paper introduces a novel approach for finding the optimal order (that data allows to estimate) of a potential Markov property. The algorithm is implemented in the package, alleviating the problem of users making Markov assumptions and implementing corresponding complex higher-order neighbourhood structures. Estimation is made accurate and stable by simultaneously utilising both Markov properties and Stein-type shrinkage. Asymptotic results on Stein-type shrinkage ensure that non-singular well conditioned matrices are obtained in an automatic manner. Final symmetry conversion creates symmetric positive definite estimates. Furthermore, the estimation routine is made efficient and scalable to very high-dimensional problems (~10^7) by utilising the sparse nature of the precision matrix under Markov assumptions. Implementation wise, the sparsity is exploited by employing the sparsity possibilities made available by the Eigen C++ linear-algebra library. The package and examples are available at https://github.com/equinor/GraphSPME
