Asymptotic Accuracy of Distribution-Based Estimation for Latent Variables

Details Asymptotic Accuracy of Distribution-Based Estimation for Latent Variables Asymptotic Accuracy of Distribution-Based Estimation for Latent Variables

2012-04-10

arxiv.org/abs/1204.2069v2

Statistics

Machine Learning

26pages, 6 figures

Scientific paper

Hierarchical statistical models are widely employed for 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. An asymptotic analysis of the models plays an important role to evaluate learning process; the analysis result is actually applied not only to theoretical but also practical situations such as the optimal model selection and the active learning. There are a lot of studies on the generalization error measuring the prediction accuracy of the observation variable. However, the accuracy of estimation for the latent variable has not been elucidated well. For the quantitative evaluation, the present paper formulates some error functions for the latent variable estimation in a distribution-based manner. Then, the asymptotic behavior is analyzed on the maximum likelihood and the Bayes methods.

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