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Open AccessArticle

Learning Coefficient of Vandermonde Matrix-Type Singularities in Model Selection

Department of Mathematics, College of Science & Technology, Nihon University, 1-8-14, Surugadai, Kanda, Chiyoda-ku, Tokyo 101-8308, Japan
Entropy 2019, 21(6), 561; https://doi.org/10.3390/e21060561
Received: 11 March 2019 / Revised: 23 May 2019 / Accepted: 29 May 2019 / Published: 4 June 2019
(This article belongs to the Special Issue Bayesian Inference and Information Theory)
In recent years, selecting appropriate learning models has become more important with the increased need to analyze learning systems, and many model selection methods have been developed. The learning coefficient in Bayesian estimation, which serves to measure the learning efficiency in singular learning models, has an important role in several information criteria. The learning coefficient in regular models is known as the dimension of the parameter space over two, while that in singular models is smaller and varies in learning models. The learning coefficient is known mathematically as the log canonical threshold. In this paper, we provide a new rational blowing-up method for obtaining these coefficients. In the application to Vandermonde matrix-type singularities, we show the efficiency of such methods. View Full-Text
Keywords: learning coefficient; Kullback function; singular learning machine; resolution of singularities learning coefficient; Kullback function; singular learning machine; resolution of singularities
MDPI and ACS Style

Aoyagi, M. Learning Coefficient of Vandermonde Matrix-Type Singularities in Model Selection. Entropy 2019, 21, 561.

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