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세미나/워크샵 게시글의 상세 화면
제목 160708_16:30_Optimal least squares method for polynomial regression and its application to Uncertainty Quantification
분류 세미나
작성자 빅데이터수리해석양성사업단 등록일 2016-07-05 조회수 344

아래와 같이 강연을 개최하오니 많은 참석 부탁드립니다.

 

일시: 07월 08일 금요일 16:30

장소: 32356

연사: 신연종 (Mathematics, University of Utah)

 

Title:

Optimal least squares method for polynomial regression and its application to Uncertainty Quantification.

 
 
In this talk, I present a quasi-optimal sample set for least squares regression. The quasioptimal set is designed in such a way that, for a given number of samples, it can deliver the regression result as close as possible to the result obtained by a (much) larger set of candidate samples. The quasi-optimal set is determined by maximizing a quantity measuring the mutual column orthogonality and the determinant of the model matrix. This procedure is non-adaptive, in the sense that it does not depend on the sample data. This is useful in practice, as it allows one to determine, prior to the potentially expensive data collection procedure, where to sample the underlying system. In addition to presenting the theoretical motivation of the optimal set, we also present its efficient implementation via a greedy algorithm, along with several numerical examples to demonstrate its efficacy. Since the quasi-optimal set allows one to obtain a near optimal regression result under any affordable number of samples, it notably outperforms other standard choices of sample sets. 
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