研究テーマ
- 非ユークリッド計算幾何学と機械学習への応用
- 学習の幾何学的構造と知能のダイナミクス
- 機械学習・データサイエンスのための幾何計算
- 情報理論とその応用
- 非類似度およびダイバージェンス（ブレグマン・ダイバージェンスを含む）
主な研究関心
研究業績・資料
幾何学的情報科学（GSI'27）の共同主催者： 2027年8月24日〜27日、フランス・トゥールーズ、ENACキャンパス。
最近のテクニカルレポート
査読付き論文としての発表に向けて準備中の研究報告です。
- Dual-connection midpoint matrix means and their Gauss composition, arXiv:2609.07551
- Minimum enclosing Bregman balls made easy, arXiv:2607.24197
- Group invariance of f-divergences and the Fisher-Rao distance, arXiv:2606.25790
- Neural Legendre-Fenchel transform with Hessian Preconditioning, arXiv:2606.09077
- Generalising maximum mean discrepancy: kernelised functional Bregman divergences, arXiv:2604.24047
- Quadratic polarity and polar Fenchel-Young divergences from the canonical Legendre polarity, arXiv:2603.04812
- Geometric structures and deviations on James' symmetric positive-definite matrix bicone domain, arXiv:2603.02483
- Scales of Fréchet means and Karcher quasi-arithmetic means, arXiv:2511.21173
- pyBregMan: A Python library for Bregman Manifolds, arXiv:2408.04175
- Tempered Calculus for ML: Application to Hyperbolic Model Embedding, arXiv:2402.04163
主な論文・著作
- PDF — The Many Faces of Information Geometry, AMS Notices, 2022. MR 4353351。 解説動画および 詳細なレビュー論文。
- Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models, Handbook of Statistics (51), Elsevier, 2024。 (arXiv)
- On f-Divergences Between Cauchy Distributions, IEEE Transactions on Information Theory, 2023。 (arXiv)
- PDF — Statistical divergences between densities of truncated exponential families with nested supports: Duo Bregman and duo Jensen divergences, Entropy, 2022。(arXiv)
- PDF — On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid, Entropy, 2022。(arXiv)
- PDF — Revisiting Chernoff information with likelihood ratio exponential families, Entropy, 2022。(arXiv)
- On conformal divergences and their population minimizers, IEEE Transactions on Information Theory 62(1), 2015。
- Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means, Pattern Recognition Letters 42, 2014。(arXiv)
- Optimal interval clustering: Application to Bregman clustering and statistical mixture learning, IEEE Signal Processing Letters 21(10), 2014。(arXiv)
- On the chi square and higher-order chi distances for approximating f-divergences, IEEE Signal Processing Letters, 2013。(arXiv)
- Jeffreys centroids: A closed-form expression for positive histograms and a guaranteed tight approximation for frequency histograms, IEEE Signal Processing Letters 20(7), 2013。
- Shape retrieval using hierarchical total Bregman soft clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012。
- The Burbea-Rao and Bhattacharyya centroids, IEEE Transactions on Information Theory, 2011。(arXiv)
- PDF — 階層的クラスタリング、Introduction to HPC with MPI for Data Science 第8章、Springer, 2016。
- A closed-form expression for the Sharma–Mittal entropy of exponential families, Journal of Physics A: Mathematical and Theoretical 45(3), 2011。(arXiv)
- Bregman Voronoi diagrams, Discrete & Computational Geometry 44, 2010。(arXiv)。 関連会議論文：On Bregman Voronoi diagrams, Proceedings of the eighteenth annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2007)。
- Hyperbolic Voronoi diagrams made easy, IEEE International Conference on Computational Science and Its Applications, 2010。(arXiv)
- Approximating smallest enclosing balls with applications to machine learning, International Journal of Computational Geometry & Applications 19(05), 2009。
