Timezone: »

Faster Principal Component Regression and Stable Matrix Chebyshev Approximation
Zeyuan Allen-Zhu · Yuanzhi Li

Tue Aug 08 01:30 AM -- 05:00 AM (PDT) @ Gallery #44
We solve principal component regression (PCR), up to a multiplicative accuracy $1+\gamma$, by reducing the problem to $\tilde{O}(\gamma^{-1})$ 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 requires $\tilde{O}(\gamma^{-2})$ 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.

Author Information

Zeyuan Allen-Zhu (Microsoft Research / Princeton / IAS)
Yuanzhi Li (Princeton University)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors