Statistical inference involving integration and optimization

在统计学中，由于归一化常数的存在，极大似然估计有时需要很大的计算量。为了避免这种计算和近年来的进展，发展了完整梯度法。在这项研究中，完整梯度方法被证明是适用于宾汉分布的，并研究了非平衡数据集上二项回归模型的行为。不平衡数据意味着应该分类的二进制标签的频率是不平衡的。在本研究中，这类数据集的模型的极限是一类特殊的Poisson点过程。

In statistics, the maximum likelihood estimation sometimes needs heavy computation due to the normalizing constant. The holonomic gradient methods are developed to avoid such computation and progress in recent years. In this research, the holonomic gradient methods are shown to be available for the Bingham distributions.Behavior of the binomial regression model for an imbalanced dataset is also investigated. The imbalanced data means that the frequency of the binary label that should be classified is imbalanced. In this research, the limit of the model for such datasets is a special class of Poisson point processes.