A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In regular statistical models, th... View more
Sumio Watanabe. Asymptotic learning curve and renormalizable condition in statistical learning theory. Journal of Physics Coneference Series, 233(1), 2010b. 012014. doi: 10.1088/1742-6596/233/1/012014.
Keisuke Yamazaki and Sumio Watanabe. Singularities in mixture models and upper bounds of stochastic complexity. Neural Networks, 16(7):1029-1038, 2003.
Keisuke Yamazaki and Sumio Watanabe. Singularities in complete bipartite graph-type boltzmann machines and upper bounds of stochastic complexities. IEEE Transactions on Neural Networks, 16(2):312-324, 2005.
Piotr Zwiernik. Asymptotic model selection and identifiability of directed tree models with hidden variables. CRiSM report, 2010.