Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
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多元高斯、半定矩阵补全和凸代数几何
DOI：
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发表时间：
2009
期刊：
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通讯作者：
Caroline Uhler
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作者：
B. Sturmfels;Caroline Uhler
我们研究了由协方差矩阵逆上的线性约束描述的多元正态模型。这种模型的最大似然估计导致了在一个面体上最大化行列式函数的问题，以及在任意线性投影下描述正定锥的图像的问题。这些问题在统计和优化的接口在这里检查从凸代数几何的角度。
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to the problem of characterizing the image of the positive definite cone under an arbitrary linear projection. These problems at the interface of statistics and optimization are here examined from the perspective of convex algebraic geometry.