Asymptotic Accuracy of Distribution-Based Estimation for Latent Variables
This work addresses a theoretical gap in evaluating latent variable accuracy, which is important for applications like optimal model selection and active learning, but it appears incremental as it extends existing asymptotic analysis from observable to latent variables.
The paper tackles the problem of evaluating the accuracy of latent variable estimation in hierarchical statistical models, which had not been previously elucidated, by formulating distribution-based error functions and analyzing their asymptotic behavior for maximum likelihood and Bayes methods.
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable labels. An asymptotic analysis of the models plays an important role in evaluating the learning process; the result of the analysis is applied not only to theoretical but also to practical situations, such as optimal model selection and active learning. There are many studies of generalization errors, which measure the prediction accuracy of the observable variables. However, the accuracy of estimating the latent variables has not yet been elucidated. For a quantitative evaluation of this, the present paper formulates distribution-based functions for the errors in the estimation of the latent variables. The asymptotic behavior is analyzed for both the maximum likelihood and the Bayes methods.