## Computing Elimination Ideals and Discriminants of Likelihood Equations. (arXiv:1810.05620v1 [cs.SC])

We develop a probabilistic algorithm for computing elimination ideals of likelihood equations, which is for larger models by far more efficient than directly computing Groebner bases or the interpolation method proposed in the first author's previous work. The efficiency is improved by a theoretical result showing that the sum of data variables appears in most coefficients of the generator polynomial of elimination ideal. Furthermore, applying the known structures of Newton polytopes of discriminants, we can also efficiently deduce discriminants of the elimination ideals. For instance, the discriminants of 3 by 3 matrix model and one Jukes-Cantor model in phylogenetics (with sizes over 30 GB and 8 GB text files, respectively) can be computed by our methods.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 We develop a probabilistic algorithm for computing elimination ideals of likelihood equations, which is for larger models by far more efficient than directly computing Groebner bases or the interpolation method proposed in the first author's previous work. The efficiency is improved by a theoretical result showing that the sum of data variables appears in most coefficients of the generator polynomial of elimination ideal. Furthermore, applying the known structures of Newton polytopes of discriminants, we can also efficiently deduce discriminants of the elimination ideals. For instance, the discriminants of 3 by 3 matrix model and one Jukes-Cantor model in phylogenetics (with sizes over 30 GB and 8 GB text files, respectively) can be computed by our methods.
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