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超逆 Wishart 矩阵的 Cholesky 分解AI 解读

The canonical parameter of a covariance selection model is the inverse covariance matrix [sum ]-1 whose zero pattern gives the conditional independence structure characterising the model. In this paper we consider the upper triangular matrix Φ obtained by the Cholesky decomposition [sum ]-1 = ΦTΦ. This provides an interesting alternative parameterisation of decomposable models since its upper triangle has the same zero structure as [sum ]-1 and its elements have an…

Isserlis 矩阵及其在不可分解高斯图模型中的应用AI 解读

The operations of matrix completion and Isserlis matrix construction arise in the statistical analysis of graphical Gaussian models, in both the Bayesian and frequentist approaches. In this paper we study the properties of the Isserlis matrix of the completion, , of a positive definite matrix and propose an edge set indexing notation which highlights the symmetry existing between and its Isserlis matrix. In this way well-known properties of can be exploited to give an easy…