We study the problem of maximizing information divergence from a new perspective using logarithmic Voronoi polytopes. We show that for linear models, the maximum is always achieved at the boundary of the probability simplex. For toric models, we present an algorithm that combines the combinatorics of the chamber complex with numerical algebraic geometry. We pay special attention to reducible models and models of maximum likelihood degree one.

翻译：我们从对数沃罗诺伊多面体的新视角研究最大化信息散度的问题。我们证明，对于线性模型，最大值总是在概率单纯形的边界处达到。对于环面模型，我们提出了一种算法，该算法将室复形的组合学与数值代数几何相结合。特别关注可约模型和最大似然度为一的模型。