Séminaire de Statistique

第0期（2025年度秋）

第1期（2026年度春）

  1. 確率過程

    キーワード：semimartingale (Métivier, 1982), Malliavin calculus (Nualart and Nualart, 2018), convergence of processes (Jacod and Shiryaev, 2003)

  2. \(\mathcal{P}(\mathbb{R}^d)\) の幾何学

    キーワード：JKO scheme (Figalli and Glaudo, 2023), Fisher-Rao geometry (Ay et al., 2017), Wasserstein geometry (Villani, 2003)

    • tempering path の Fisher-Rao 幾何に関する解析 (Aubin-Frankowski et al., 2022), (Chopin et al., 2023) の証明を，Wasserstein 幾何に関する勾配流の枠組みと同様に，勾配流の数学 (Ambrosio et al., 2008) を通じて定式化できないか？

    • 平均場 Langevin 拡散の \(\mathcal{P}(\mathbb{R}^d)\) 勾配流としての解釈．

    • (Hoffman and Ma, 2020) の過程を \(d\to\infty\) の極限をとったら，変化点を持つ過程に収束する？最適化とサンプリングの中間を取れば，特定の分布族の中で KL の意味で真の分布との距離を最小にする点に収束する？

  3. 統計的学習理論

    キーワード：empirical process (Giné and Nickl, 2021), learning theory (Bach, 2024), PAC-Bayes (Alquier, 2024)

    • 早期停止に関する研究（離散拡散モデル (Zhang et al., 2024), ロジスティック回帰 (Wu et al., 2025) ）はリスク評価を各時点（早期停止点や収束点など）に対して静的に行っているのみである．理論の確率過程化ができないか？

    • SGD path を追う研究 (Glasgow, 2024), (Berthier et al., 2024) もまだ静的な・停止時を用いた解析にとどまっている．

2025 夏

Location Time
ISM 3F -

References

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