Critical Lines in Symmetry of Mixture Models and its Application to Component Splitting

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

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Kenji Fukumizu, Shotaro Akaho, Shun-ichi Amari


We show the existence of critical points as lines for the likelihood func- tion of mixture-type models. They are given by embedding of a critical point for models with less components. A sufficient condition that the critical line gives local maxima or saddle points is also derived. Based on this fact, a component-split method is proposed for a mixture of Gaus- sian components, and its effectiveness is verified through experiments.