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**1 - 1**of**1**### Asymptotic Theory of Locally Conic Models and its Applications to Neural Networks

, 2001

"... Abstract: Multilayer neural networks have a problem of unidentiÞability in its parameter-ization. If a network has surplus hidden units to realize a target function, the parameters to give the function consist of a high dimensional subset. Many of usual statistical views fail in such cases. This pap ..."

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Abstract: Multilayer neural networks have a problem of unidentiÞability in its parameter-ization. If a network has surplus hidden units to realize a target function, the parameters to give the function consist of a high dimensional subset. Many of usual statistical views fail in such cases. This paper discusses the likelihood ratio of the maximum likelihood es-timation in unidentiÞable cases, using the framework of locally conic models. We derive a sufficient condition that the likelihood ratio has a larger order than usual Op(1). The exact order of the likelihood ratio of multilayer perceptrons is derived, and a new regularization scheme is proposed to overcome the strong overÞtting.