東京確率論セミナー

過去の記録 ~04/16次回の予定今後の予定 04/17~

開催情報 月曜日 16:00~17:30 数理科学研究科棟(駒場) 126号室
担当者 佐々田槙子、中島秀太(明治大学)
セミナーURL https://sites.google.com/view/tokyo-probability-seminar23/2024年度

2023年08月07日(月)

17:00-18:30   数理科学研究科棟(駒場) 123号室
いつもと教室が異なります.
Freddy Delbaen 氏 (Professor emeritus at ETH Zurich)
Approximation of Random Variables by Elements that are independent of a given sigma algebra (English)
[ 講演概要 ]
Given a square integrable m-dimensional random variable $X$ on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and a sub sigma algebra $\mathcal{A}$, we show that there exists another m-dimensional random variable $Y$, independent of $\mathcal{A}$ and minimising the $L^2$ distance to $X$. Such results have an importance to fairness and bias reduction in Artificial Intelligence, Machine Learning and Network Theory. The proof needs elements from transportation theory, a parametric version due to Dudley and Blackwell of the Skorohod theorem, selection theorems, … The problem also triggers other approximation problems. (joint work with C. Majumdar)