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

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.