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【GIR公開セミナー】Dr. Nicki Holighaus / オーストリア科学アカデミー(オーストリア)

日時 2025.2.10(13:00~14:30)
会場

東京農工大学 ⼩⾦井キャンパス 3号館 2階 204室

Zoom

ミーティングID:836 4540 7210

パスコード:602184

Google Classroom コード fmk5ljl
講演者 Dr. Nicki Holighaus
所属機関 オーストリア科学アカデミー (オーストリア)
講演タイトル "Fundamentals of Quasi-Monte Carlo Integration"

<要旨>
The Monte Carlo (MC) method is a simple quadrature rule for the approximation of integrals over finite domain or, more generally, probability spaces. Specifically, MC simply approximates an integral by the mean of finitely many samples, taken uniformly at random in the domain of integration. MC is very simple, but only achieves an approximation rate of O(N-1/2), in expectation. Quasi-Monte Carlo (QMC) likewise approximates integrals by the mean of point evaluations, eschewing random points in favor of point sets that are, in an appropriate sense, well-distributed. The Koksma-Hlawka inequality provides a worst-case bound of the integration error in QMC in the form D(P)S(f), where D(P) is a measure of equidistribution of the samples P, usually referred to as discrepancy and S(f) is a measure of smoothness of the integrand f. Crucially, there are sets P that achieve discrepancy of order O(log(N)d/N), significantly improving convergence speed over MC.

In this talk, we cover fundamental concepts of QMC, such as Koksma-Hlawka-type error bounds and appropriate measures of discrepancy and smoothness. On the d-dimensional unit square, we will illustrate some constructions of point sets and sequences with low discrepancy.

To illustrate that measuring equidistribution of a finite set of points in a domain is somewhat subjective and not necessarily straightforward, I prepared a short survey in which you can test your own intuition on the subject, leading up to the presentation: https://forms.gle/TgfGeexRevajNJMM8 (less than 5 minutes). I will shortly discuss the survey results at the beginning and end of the talk.
言語 英語
対象 どなたでも、ご参加いただけます。
主催 グローバルイノベーション研究院 ライフサイエンス分野 矢田部チーム
卓越大学院プログラム
お問い合わせ窓口 グローバルイノベーション研究院・工学研究院 矢田部 浩平
e-mail: yatabe(ここに@ を入れてください)go.tuat.ac.jp
備考

本セミナーは、オンライン・対面型の同時開催となります。
後日、Google Classroomでも公開いたします。

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