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Accuracy of latent variable estimation with the maximum likelihood estimator for partially observed hidden data

机译:最大似然估计器对部分观测到的隐藏数据的潜在变量估计的准确性

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摘要

Hierarchical statistical models are widely applied to information science and data engineering. The models consist of two variables: an observable variable for the given data and a latent variable for an unobservable label. There are a lot of analysis results on the generalization error measuring the prediction accuracy of the observation variable. However, the accuracy of estimation for the latent variable has not been studied well. In the previous study, an error function for the latent variable was formulated, and the asymptotic behavior was analyzed on the maximum likelihood estimation. The present paper extends the analysis method to the semi-supervised learning, where the labels are available in some parts of data, and reveals the asymptotic form of the error function.
机译:分层统计模型已广泛应用于信息科学和数据工程。模型由两个变量组成:给定数据的可观察变量和不可观察的标签的潜在变量。关于测量观测变量的预测精度的泛化误差,有很多分析结果。但是,潜在变量的估计精度尚未得到很好的研究。在先前的研究中,对潜在变量建立了误差函数,并根据最大似然估计分析了渐近行为。本文将分析方法扩展到半监督学习,其中在部分数据中可用标签,并揭示误差函数的渐近形式。

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