Many machine learning algorithms require the summation of Gaussian kernel
functions, an expensive operation if implemented straightforwardly. Several methods
have been proposed to reduce the computational complexity of evaluating such
sums, including tree and analysis based methods. These achieve varying speedups
depending on the bandwidth, dimension, and prescribed error, making the choice
between methods difficult for machine learning tasks. We provide an algorithm
that combines tree methods with the Improved Fast Gauss Transform (IFGT). As
originally proposed the IFGT suffers from two problems: (1) the Taylor series
expansion does not perform well for very low bandwidths, and (2) parameter selection
is not trivial and can drastically affect performance and ease of use. We
address the first problem by employing a tree data structure, resulting in four evaluation
methods whose performance varies based on the distribution of sources and
targets and input parameters such as ...
Vlad I. Morariu1, Balaji V. Srinivasan, Vikas C. R