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Tokyo Probability Seminar
Seminar information archive ～06/08｜Next seminar｜Future seminars 06/09～
| Date, time & place | Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima, Masato Hoshino |
2023/08/07
17:00-18:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Freddy Delbaen (Professor emeritus at ETH Zurich)
Approximation of Random Variables by Elements that are independent of a given sigma algebra (English)
Freddy Delbaen (Professor emeritus at ETH Zurich)
Approximation of Random Variables by Elements that are independent of a given sigma algebra (English)
[ Abstract ]
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)
