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Singularities in complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities

机译:完全二部图型Boltzmann机的奇异性和随机复杂度的上限

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It is well known that Boltzmann machines are nonregular statistical models. The set of their parameters for a small size model is an analytic set with singularities in the space of a large size one. The mathematical foundation of their learning is not yet constructed because of these singularities, though they are applied to information engineering. Recently we established a method to calculate the Bayes generalization errors using an algebraic geometric method even if the models are nonregular. This paper clarifies that the upper bounds of generalization errors in Boltzmann machines are smaller than those in regular statistical models.
机译:众所周知,玻耳兹曼机是非正规的统计模型。小尺寸模型的参数集是在大尺寸空间中具有奇点的解析集。尽管这些奇异性已应用到信息工程中,但由于这些奇异性,他们的学习的数学基础尚未构建。最近,我们建立了一种使用代数几何方法计算贝叶斯泛化误差的方法,即使模型是非正规的。本文阐明,玻尔兹曼机的广义误差上限小于常规统计模型中的广义误差上限。

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