Structure Learning Theory and Birational Geometry

2014 Fiscal Year Final Research Report

• Project/Area Number: 23500172
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Intelligent informatics
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: WATANABE SUMIO 東京工業大学, 総合理工学研究科(研究院), 教授 (80273118)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 双有理幾何学 / 構造学習理論 / ベイズ自由エネルギー / WBIC / 双有理不変量

Outline of Final Research Achievements

In statistical machine learning, it is well known that the appropriate model and prior for a given set of training samples is chosen by minimization of the Bayesian free energy. However, there has been no method to estimate the Bayesian free energy if the posterior distribution can not be approximated by any normal distribution. In this research, we created a new concept, a widely applicable Bayesian information criterion (WBIC), and proved that WBIC has the same asymptotic behavior as the Bayesian free energy, based on the birational geometry. The obtained theorem enables us to choose the optimal model for a given set of training samples, even if the model has hierarchical structures.

Free Research Field

数理情報学