论文标题
关于连续分配的归一化常量
On the Normalizing Constant of the Continuous Categorical Distribution
论文作者
论文摘要
SimpleX上支持的概率分布在统计和机器学习中享有广泛的应用。最近，已经发现了一个新颖的这种分布家族：连续的分类。这个家庭享有非凡的数学简单性。它的密度函数类似于Dirichlet分布的函数，但具有归一化常数，只能使用基本功能以封闭形式写入。尽管具有这种数学简单性，但我们对归一化常数的理解远非完整。在这项工作中，我们表征了归一化常数的数值行为，并提出了理论和方法学的进步，从而有助于实现连续分类分布的更广泛应用。我们的代码可从https://github.com/cunningham-lab/cb_and_cc/获得。
Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys remarkable mathematical simplicity; its density function resembles that of the Dirichlet distribution, but with a normalizing constant that can be written in closed form using elementary functions only. In spite of this mathematical simplicity, our understanding of the normalizing constant remains far from complete. In this work, we characterize the numerical behavior of the normalizing constant and we present theoretical and methodological advances that can, in turn, help to enable broader applications of the continuous categorical distribution. Our code is available at https://github.com/cunningham-lab/cb_and_cc/.
