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.
['Yeonjong Shin', 'Dongbin Xiu']
On a near optimal sampling strategy for least squares polynomial regression