稀疏多项式系统的最大似然度

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-05-16 DOI:10.1137/21m1422550

J. Lindberg, Nathan Nicholson, J. Rodriguez, Zinan Wang

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引用次数: 3

摘要

我们考虑由具有一般系数的稀疏多项式系统的公共解集产生的统计模型。最大似然度计算模型限定的似然函数的临界点的个数。我们证明了一个稀疏多项式系统的最大似然度是由它的牛顿多体决定的，并且等于一个相关的拉格朗日方程组的混合体积。

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The Maximum Likelihood Degree of Sparse Polynomial Systems

We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of critical points of the likelihood function restricted to the model. We prove the maximum likelihood degree of a sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.

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来源期刊

SIAM Journal on Applied Algebra and Geometry MATHEMATICS, APPLIED-

CiteScore

2.20

自引率

0.00%

发文量