论文标题
对称矩阵的线性空间的最大似然度
The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices
论文作者
论文摘要
我们研究了浓度矩阵上线性条件描述的多元高斯模型。我们计算这些模型的最大似然度（ML）度。也就是说，我们在对称矩阵的线性空间上计算了可能性函数的临界点。我们获得了ML程度的新公式，一个通过Schubert演算获得了相交理论中的Segre类。我们解决了Codimension One模型的情况，并在ML度为零时表征了退化情况。
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over a linear space of symmetric matrices. We obtain new formulae for the ML degree, one via Schubert calculus, and another using Segre classes from intersection theory. We settle the case of codimension one models, and characterize the degenerate case when the ML degree is zero.
