| Abstract | Algorithms based on kernel methods play a central rolein statistical machine learning. At their core are a num-
ber of linear algebra operations on matrices of kernel
functions which take as arguments the training and test-
ing data. These range from the simple matrix-vector
product, to more complex matrix decompositions, and
iterative formulations of these. Often the algorithms
scale quadratically or cubically, both in memory and op-
erational complexity, and as data sizes increase, kernel
methods scale poorly. We use parallelized approaches
on a multi-core graphical processor (GPU) to partially
address this lack of scalability. GPUs are used to scale
three different classes of problems, a simple kernel-
matrix-vector product, iterative solution of linear sys-
tems of kernel function and QR and Cholesky decom-
position of kernel matrices. Application of these accel-
erated approaches in scaling several kernel based learn-
ing approaches are shown, and in each case substantial
speedups are obtained. The core software is released as
an open source package, GPUML.
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