Neural Comput - Learning coefficient of generalization error in Bayesian estimation and vandermonde matrix-type singularity.

Tópicos

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Resumo

The term algebraic statistics arises from the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry (Sturmfels, 2009 ). The purpose of our study is to consider the generalization error and stochastic complexity in learning theory by using the log-canonical threshold in algebraic geometry. Such thresholds correspond to the main term of the generalization error in Bayesian estimation, which is called a learning coefficient (Watanabe, 2001a , 2001b ). The learning coefficient serves to measure the learning efficiencies in hierarchical learning models. In this letter, we consider learning coefficients for Vandermonde matrix-type singularities, by using a new approach: focusing on the generators of the ideal, which defines singularities. We give tight new bound values of learning coefficients for the Vandermonde matrix-type singularities and the explicit values with certain conditions. By applying our results, we can show the learning coefficients of three-layered neural networks and normal mixture models.

Resumo Limpo

term algebra statist aris studi probabilist model techniqu statist infer use method algebra geometri sturmfel purpos studi consid general error stochast complex learn theori use logcanon threshold algebra geometri threshold correspond main term general error bayesian estim call learn coeffici watanab b learn coeffici serv measur learn effici hierarch learn model letter consid learn coeffici vandermond matrixtyp singular use new approach focus generat ideal defin singular give tight new bound valu learn coeffici vandermond matrixtyp singular explicit valu certain condit appli result can show learn coeffici threelay neural network normal mixtur model

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