大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Approximation of Random Variables by Elements that are Independent of a given Sigma-Algebra

Freddy Delbaen (ETH Zurich)

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4. Approximation of Random Variables by Elements that are Independent of a given Sigma-Algebra

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第136回

Approximation of Random Variables by Elements that are Independent of a given Sigma-Algebra

Freddy Delbaen (ETH Zurich)

Given a square integrable m-dimensional random variable $X$ on a probability space $(\Omega,\Fc,\Pr)$ and a sub sigma algebra $\Ac$, we show that there exists another m-dimensional random variable $Y$, independent of $\Ac$ 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 of the Skorohod theorem due to Dudley and Blackwell, selection theorems, … The problem also triggers other approximation problems.

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