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贝叶斯半监督学习中潜在变量估计的准确性。

Accuracy of latent-variable estimation in Bayesian semi-supervised learning.

机构信息

Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G5-19 4259 Nagatsuta Midori-ku Yokohama, Japan.

出版信息

Neural Netw. 2015 Sep;69:1-10. doi: 10.1016/j.neunet.2015.04.012. Epub 2015 May 9.

Abstract

Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysis, are regarded as estimations of latent variables based on the observable ones. The estimation of latent variables in semi-supervised learning, where some labels are observed, will be more precise than that in unsupervised, and one of the concerns is to clarify the effect of the labeled data. However, there has not been sufficient theoretical analysis of the accuracy of the estimation of latent variables. In a previous study, a distribution-based error function was formulated, and its asymptotic form was calculated for unsupervised learning with generative models. It has been shown that, for the estimation of latent variables, the Bayes method is more accurate than the maximum-likelihood method. The present paper reveals the asymptotic forms of the error function in Bayesian semi-supervised learning for both discriminative and generative models. The results show that the generative model, which uses all of the given data, performs better when the model is well specified.

摘要

分层概率模型,如高斯混合模型,被广泛应用于无监督学习任务。这些模型由可观测变量和潜在变量组成,分别代表可观测数据和潜在的数据生成过程。无监督学习任务,如聚类分析,被视为基于可观测变量对潜在变量的估计。在半监督学习中,一些标签是可观测的,对潜在变量的估计会比无监督学习更精确,其中一个关注点是澄清标记数据的影响。然而,对于潜在变量估计的准确性,还没有足够的理论分析。在之前的研究中,提出了一种基于分布的误差函数,并计算了生成模型的无监督学习的渐近形式。已经表明,对于潜在变量的估计,贝叶斯方法比最大似然方法更准确。本文揭示了判别和生成模型的贝叶斯半监督学习中误差函数的渐近形式。结果表明,在模型指定良好的情况下,使用所有给定数据的生成模型表现更好。

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