On a near optimal sampling strategy for least squares polynomial regression

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• 作者：Yeonjong Shin ^{shin.481@osu.edu" class="auth_mail" title="E-mail the corresponding author} ; Dongbin Xiu ; ^{xiu.16@osu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Polynomial regression ; Least squares ; Christoffel function
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：326
• 期：Complete
• 页码：931-946
• 全文大小：794 K

文摘

We present a sampling strategy of least squares polynomial regression. The strategy combines two recently developed methods for least squares method: Christoffel least squares algorithm and quasi-optimal sampling. More specifically, our new strategy first choose samples from the pluripotential equilibrium measure and then re-order the samples by the quasi-optimal algorithm. A weighted least squares problem is solved on a (much) smaller sample set to obtain the regression result. It is then demonstrated that the new strategy results in a polynomial least squares method with high accuracy and robust stability at almost minimal number of samples.