Research and development of nonlinear Selective Inference for high-dimensional and small number of samples data

2023 Fiscal Year Final Research Report

• Project/Area Number: 20H04243
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 61030:Intelligent informatics-related
• Research Institution: Okinawa Institute of Science and Technology Graduate University (2023); Kyoto University (2020-2022)
• Principal Investigator: Yamada Makoto 沖縄科学技術大学院大学, 機械学習とデータ科学ユニット, 准教授 (00581323)
• Co-Investigator(Kenkyū-buntansha): 下平 英寿 京都大学, 情報学研究科, 教授 (00290867) ; POIGNARD BENJAMIN 大阪大学, 大学院経済学研究科, 准教授 (40845252)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 選択的推論 / 特徴選択

Outline of Final Research Achievements

In this research, we worked on a high-dimensional extension of nonlinear selective inference. In FY2020, we developed a statistical hypothesis testing method using HSIC Lasso and the Split method, and demonstrated its effectiveness on real data. In FY2021, we proposed a method based on HSIC with Polyhedral Lemma and Knockoff filter, which were reported in ICML 2021 and AISTATS 2022, respectively. In the fiscal year 2022, we proposed a new high-dimensional data analysis method based on the optimal transport method, which was presented at AISTATS 2022 and TMLR, respectively. In the final year, we proposed the Distance Covariance Lasso method and showed the theoretical properties of selective inference.

Free Research Field

機械学習

Academic Significance and Societal Importance of the Research Achievements

本研究は、非線形選択的推論を高次元データに適用する新たな手法を提案し, 統計的仮説検定の検出力向上を目指した. 　さらに, 木構造最適輸送に基づくBarycenterの推定手法やWasserstein距離の学習方法など, 新たな高次元データ解析手法を開発した. つまり, 我々は非線形データの特徴選択とスクリーニングの理論的基盤を確立したと言える. さらに今後, 機械学習やバイオインフォマティクス分野での実用的な応用され, 提案法による新規の科学的発見が期待できる. これらの成果は、学術的意義に加え、社会的にも広範な影響を与えると考える.