对数线性模型中最大似然估计的环不变理论

Carlos Am'endola, Kathlén Kohn, Philipp Reichenbach, A. Seigal
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引用次数: 6

摘要

建立了离散统计模型的不变量理论与最大似然估计之间的联系。我们证明了环面轨道上的范数最小化等价于对数线性模型中的极大似然估计。我们使用环面作用下的稳定性概念来表征最大似然估计的存在性,并讨论了与缩放算法的联系。
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Toric invariant theory for maximum likelihood estimation in log-linear models
We establish connections between invariant theory and maximum likelihood estimation for discrete statistical models. We show that norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We use notions of stability under a torus action to characterize the existence of the maximum likelihood estimate, and discuss connections to scaling algorithms.
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Journal of Algebraic Statistics
Journal of Algebraic Statistics STATISTICS & PROBABILITY-
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