  Kernel methods are ubiquitous tools in machine learning. However, there is
often little reason for the common practice of selecting a kernel a priori.
Even if a universal approximating kernel is selected, the quality of the finite
sample estimator may be greatly affected by the choice of kernel. Furthermore,
when directly applying kernel methods, one typically needs to compute a $N
\times N$ Gram matrix of pairwise kernel evaluations to work with a dataset of
$N$ instances. The computation of this Gram matrix precludes the direct
application of kernel methods on large datasets, and makes kernel learning
especially difficult. In this paper we introduce Bayesian nonparmetric
kernel-learning (BaNK), a generic, data-driven framework for scalable learning
of kernels. BaNK places a nonparametric prior on the spectral distribution of
random frequencies allowing it to both learn kernels and scale to large
datasets. We show that this framework can be used for large scale regression
and classification tasks. Furthermore, we show that BaNK outperforms several
other scalable approaches for kernel learning on a variety of real world
datasets.
