Inference via functional theory and L1 regularization modeling

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610035
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Chuo University
• Principal Investigator: Konishi Sadanori 中央大学, 理工学部, 教授 (40090550)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: スパースモデリング / ベイズモデリング / 非線形モデリング / 混合効果モデリング / モデル評価基準 / 汎関数理論

Outline of Final Research Achievements

In various fields of science and industry a huge amount of data with complex structure and/or high-dimensional data have been accumulating. The effective use of these data sets requires new modeling strategies in order to perform extraction of useful information and knowledge discovery. Through this research we have investigated the problem of analyzing such datasets, and proposed various statistical modeling strategies: (1) Various regularization methods with L1 norm penalty have been proposed for effective regression modeling from a Bayesian point of view. (2) For analyzing data with complicated structure or substantial longitudinal heterogeneity between subjects, we introduced a varying coefficient modeling and a nonlinear functional mixed modeling through the nonlinear regression approach. (3) We developed a general framework for constructing model selection criteria in the context of functional statistics.

Free Research Field

統計科学