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東京確率論セミナー
過去の記録 ～05/21｜次回の予定｜今後の予定 05/22～
| 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）、星野壮登（東京科学大学） |
| セミナーURL | https://sites.google.com/view/tokyo-probability-seminar23/ |
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)
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 (Ω,F,P) and a sub sigma algebra A, we show that there exists another m-dimensional random variable Y, independent of A and minimising the L2 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)
Given a square integrable m-dimensional random variable X on a probability space (Ω,F,P) and a sub sigma algebra A, we show that there exists another m-dimensional random variable Y, independent of A and minimising the L2 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)
