English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Hierarchical parametric models consisting of observable and latent variablesare widely used for unsupervised learning tasks. For example, a mixture modelis a representative hierarchical model for clustering. From the statisticalpoint of view, the models can be regular or singular due to the distribution ofdata. In the regular case, the models have the identifiability; there isone-to-one relation between a probability density function for the modelexpression and the parameter. The Fisher information matrix is positivedefinite, and the estimation accuracy of both observable and latent variableshas been studied. In the singular case, on the other hand, the models are notidentifiable and the Fisher matrix is not positive definite. Conventionalstatistical analysis based on the inverse Fisher matrix is not applicable.Recently, an algebraic geometrical analysis has been developed and is used toelucidate the Bayes estimation of observable variables. The present paperapplies this analysis to latent-variable estimation and determines itstheoretical performance. Our results clarify behavior of the convergence of theposterior distribution. It is found that the posterior of theobservable-variable estimation can be different from the one in thelatent-variable estimation. Because of the difference, the Markov chain MonteCarlo method based on the parameter and the latent variable cannot constructthe desired posterior distribution.

Asymptotic Accuracy of Bayes Estimation for Latent Variables with Redundancy