论文标题
具有非最大最大似然度的对称矩阵的线性空间
Linear Spaces of Symmetric Matrices with Non-Maximal Maximum Likelihood Degree
论文作者
论文摘要
我们研究代数统计中线性浓度模型的最大似然度。我们将互惠品种的几何形状与半决赛编程的几何形状联系起来。我们表明，Zariski在法术中的Zariski闭合是线性空间集的一组，这些空间无法达到其最大可能的最大似然度，这与一组线性空间的Zariski闭合相吻合，该线性空间定义了一个阳性半菲尼特锥体的未闭合图像。特别是，这表明这种封闭是共截相性超曲面的结合。
We study the maximum likelihood degree of linear concentration models in algebraic statistics. We relate the geometry of the reciprocal variety to that of semidefinite programming. We show that the Zariski closure in the Grassmanian of the set of linear spaces that do not attain their maximal possible maximum likelihood degree coincides with the Zariski closure of the set of linear spaces defining a projection with non-closed image of the positive semidefinite cone. In particular, this shows that this closure is a union of coisotropic hypersurfaces.
