It is well known that mixture models such as gaussian mixtures are non-regular statistical models, since the set of parameters of small size models is an analytic set with singularities in the apace of parameters of a large size models. Because of these singularities, the mathematical foundation of the models is not yet constructed though the models are applied in a lot of information processing systems. Recent years using the algebraic geometrical method, we can calculate the stochastic complexity that is the roost important value to clarify the models. This paper proves the theorem that shows the tipper hounds of it in mixture models with the method.
展开▼
