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Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of view, the models can be regular or singular due to the distribution of data. In the regular case, the models have the identifiability; there is one-to-one relation...
Hidden Markov models are widely used for modeling underlying dynamics of sequence data. The accurate hidden state estimation is one of the central issues on practical application since the dynamics is described as a sequence of hidden states. However, while there are many studies on parameter estimation, mathematical properties of the hidden state estimation have not been clarified yet. The present...
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