论文标题
多项式混合物中贝叶斯泛化误差的渐近行为
Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures
论文作者
论文摘要
多项式混合物被广泛用于信息工程领域，但是，由于它们是单一的学习模型，因此尚未阐明它们的数学属性。实际上，这些模型是不可识别的，其Fisher信息矩阵并不确定。近年来，通过使用代数几何方法来阐明单数统计模型的数学基础。在本文中，我们阐明了多项式混合物的真实对数规范阈值和多重性，并阐明了其概括误差和自由能的渐近行为。
Multinomial mixtures are widely used in the information engineering field, however, their mathematical properties are not yet clarified because they are singular learning models. In fact, the models are non-identifiable and their Fisher information matrices are not positive definite. In recent years, the mathematical foundation of singular statistical models are clarified by using algebraic geometric methods. In this paper, we clarify the real log canonical thresholds and multiplicities of the multinomial mixtures and elucidate their asymptotic behaviors of generalization error and free energy.
