High-Dimensional Nonlinear Feature Selection with Hilbert-Schmidt Independence Criterion Lasso
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- Yamada Makoto
- 沖縄科学技術大学院大学 京都大学情報学研究科 理化学研究所革新知能統合研究センター
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- Poignard Benjamin
- 理化学研究所革新知能統合研究センター 大阪大学経済学研究科
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- Yamada Hiroaki
- 京都大学情報学研究科
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- Freidling Tobias
- University of Cambridge
Bibliographic Information
- Other Title
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- Hilbert-Schmidt Independence Criterion Lasso法に基づいた高次元非線形特徴選択
- Hilbert-Schmidt Independence Criterion Lasso ホウ ニ モトズイタ コウジゲン ヒセンケイ トクチョウ センタク
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Abstract
<p>Variable selection is a significant research topic in the statistics, machine learning and data mining communities. In statistics, statistical methods based on sparse modeling and sure independence screening (SIS) are major research topics for feature selection problems. However, most of the feature selection methods developed in the machine learning community lack of theoretical guarantees. Hence, these feature selection methods have been overlooked by the statistics community, despite their good prediction accuracy usually obtained in real/simulated experiments. In this paper, we introduce the so-called Hilbert-Schmidt Independence Criterion Lasso (HSIC Lasso), a feature selection method widely used among the machine learning and data mining communities. First, we introduce the HSIC Lasso as a feature selection method and derive the related convex optimization problem. Then, we describe the Block HSIC Lasso procedure together with the related selective inference framework. Furthermore, we show that the HSIC Lasso is closely related to the nonnegative Lasso and the HSIC-based SIS. Finally, we provide some large sample properties of the HSIC Lasso.</p>
Journal
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- Journal of the Japan Statistical Society, Japanese Issue
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Journal of the Japan Statistical Society, Japanese Issue 53 (1), 49-67, 2023-09-07
Japan Statistical Society
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Details 詳細情報について
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- CRID
- 1390578847123969024
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- NII Book ID
- AA1105098X
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- ISSN
- 21891478
- 03895602
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- NDL BIB ID
- 033071903
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
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- Abstract License Flag
- Disallowed