论文标题
beta-liouville多项式的快速最大似然估计和监督分类
Fast Maximum Likelihood Estimation and Supervised Classification for the Beta-Liouville Multinomial
论文作者
论文摘要
多项式和相关的分布长期以来一直用于模拟从生物信息学到自然语言处理的领域中基于计数的数据。由于其计算效率和直接的参数估计过程，通常使用的变体包括标准的多项式和Dirichlet多项式分布。但是，这些分布对被建模的分类特征之间的平均值，方差和协方差提出了严格的假设。如果数据未达到这些假设，则可能导致参数估计值和下游应用等分类等准确性损失。在这里，我们使用称为beta-liouville多项式的替代分布探索有效的参数估计和监督分类方法，该分布放松了一些多项式假设。我们表明，对于牛顿 - 拉夫森的最大似然估计，Beta-liouville多项式与Dirichlet的效率相当，并且其在模拟数据上的性能匹配或超过了多项式和Dirichlet多项式分布的效率。最后，我们证明了Beta-liouville多项式在四个金标准数据集中的两个上优于多项式和迪里奇的多项式多项式，从而支持其在监督分类上下文中具有低至中等类重叠的模拟数据中的使用。
The multinomial and related distributions have long been used to model categorical, count-based data in fields ranging from bioinformatics to natural language processing. Commonly utilized variants include the standard multinomial and the Dirichlet multinomial distributions due to their computational efficiency and straightforward parameter estimation process. However, these distributions make strict assumptions about the mean, variance, and covariance between the categorical features being modeled. If these assumptions are not met by the data, it may result in poor parameter estimates and loss in accuracy for downstream applications like classification. Here, we explore efficient parameter estimation and supervised classification methods using an alternative distribution, called the Beta-Liouville multinomial, which relaxes some of the multinomial assumptions. We show that the Beta-Liouville multinomial is comparable in efficiency to the Dirichlet multinomial for Newton-Raphson maximum likelihood estimation, and that its performance on simulated data matches or exceeds that of the multinomial and Dirichlet multinomial distributions. Finally, we demonstrate that the Beta-Liouville multinomial outperforms the multinomial and Dirichlet multinomial on two out of four gold standard datasets, supporting its use in modeling data with low to medium class overlap in a supervised classification context.
