  The computational complexity of kernel methods has often been a major barrier
for applying them to large-scale learning problems. We argue that this barrier
can be effectively overcome. In particular, we develop methods to scale up
kernel models to successfully tackle large-scale learning problems that are so
far only approachable by deep learning architectures. Based on the seminal work
by Rahimi and Recht on approximating kernel functions with features derived
from random projections, we advance the state-of-the-art by proposing methods
that can efficiently train models with hundreds of millions of parameters, and
learn optimal representations from multiple kernels. We conduct extensive
empirical studies on problems from image recognition and automatic speech
recognition, and show that the performance of our kernel models matches that of
well-engineered deep neural nets (DNNs). To the best of our knowledge, this is
the first time that a direct comparison between these two methods on
large-scale problems is reported. Our kernel methods have several appealing
properties: training with convex optimization, cost for training a single model
comparable to DNNs, and significantly reduced total cost due to fewer
hyperparameters to tune for model selection. Our contrastive study between
these two very different but equally competitive models sheds light on
fundamental questions such as how to learn good representations.
