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》 资源 》论文》Faster Principal Component Regression and Stable Matrix Chebyshev Approximation

Faster Principal Component Regression and Stable Matrix Chebyshev Approximation

2020-03-09 | |  65 |   36 |   0

Abstract

We solve principal component regression (PCR), up to a multiplicative accuracy 1+γ, by reducing the problem to 图片.png black-box calls of ridge regression. Therefore, our algorithm does not require any explicit construction of the top principal components, and is suitable for large-scale PCR instances. In contrast, previous result reequires 图片.png  such black-box calls. We obtain  this result by developing a general stable recurrence formula for matrix Chebyshev polynomials, and a degree-optimal polynomial approximation to the matrix sign function. Our techniques may be of independent interests, especially when designing iterative methods.

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