“Error rates for kernel methods under source and capacity conditions”
September 7, 2022 | Time 11:30am CET
We investigate the rates of decay of the prediction error for kernel methods under the Gaussian design and source/capacity assumptions. For kernel ridge regression, we derive all the observable rates, and characterize the regimes in which each hold. In particular, we show that the decay rate may transition from a fast, noiseless rate to a slow, noisy rate as the sample complexity is increased. For noiseless kernel classification, we derive the rates for two standard classifiers, margin-maximizing SVMs and ridge classifiers, and contrast the two methods. In both cases, the derived rates also describe to a good degree the learning curves of a number of real datasets. This is joint work with Bruno Loureiro, Florent Krzakala and Lenka Zeborová.
Hugo Cui is currently a PhD student in the Statistical Physics of Computation lab in EPFL, Switzerland. He previously studied theoretical physics at ENS Paris.