Variable Selection for Small Sample and High Dimension Case by Semi-supervised Learning and Its Application to Super-Resolution

2016 Fiscal Year Final Research Report

• Project/Area Number: 25870503
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science; Perceptual information processing
• Research Institution: Kyushu University
• Principal Investigator: Kawakita Masanori 九州大学, システム情報科学研究院, 助教 (90435496)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 半教師付き学習 / MDL原理 / 超解像 / Barron and Cover理論 / スパースコーディング

Outline of Final Research Achievements

The main important result of this study is that we provided a way to extend Barron and Cover’s theory to supervised learning without any significant lack of its virtues, which had been considered to be difficult. Our extension leads to a risk estimator of supervised learning without conventional assumptions like boundedness of random variables and/or asymptotic assumption. By our method, we succeeded in deriving a new risk bound of the most famous compressed sensing algorithm (lasso). We also extended these results to semi-supervised learning and sparse coding. Furthermore, by implementing semi-supervised sparse coding, we construct a new semi-supervised super-resolution algorithm. We show that the accuracy of super-resolution can be improved by semi-supervised super-resolution by numerical experiments though its extent strongly depends on input images.

Free Research Field

統計科学，機械学習，情報理論