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Title
Japanese:一般ディリクレ分布を用いた混合正規分布の変分自由エネルギーの漸近挙動について 
English:Asymptotic Behavior of Variational Free Energy for Normal Mixtures Using General Dirichlet Distribution 
Author
Japanese: 中村文士, 渡辺澄夫.  
English: Fumito Nakamura, Sumio Watanabe.  
Language Japanese 
Journal/Book name
Japanese:電子情報通信学会論文誌. D, 情報・システム 
English:IEICE Transactions on Information and Systems 
Volume, Number, Page Vol. 97.5    No. 5    pp. 1001-1013
Published date May 1, 2014 
Publisher
Japanese: 
English: 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
Abstract The variational Bayes learning approximates the Bayes posterior distribution with smaller computational costs. Its theoretical property is now being clarified, however, the asymptotic behavior of the variational free energies in general cases are still unknown. In this paper, we clarify the upper and lower bounds of asymptotic variational free energy when hyperparameters in the Dirichlet distribution are different from each other. We show that our result contains the conventional researches as special cases and that the variational Bayes learning has a phase transition with respect to the hyperparameter control.

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