  While tree methods have been popular in practice, researchers and
practitioners are also looking for simple algorithms which can reach similar
accuracy of trees. In 2010, (Ping Li UAI'10) developed the method of
"abc-robust-logitboost" and compared it with other supervised learning methods
on datasets used by the deep learning literature. In this study, we propose a
series of "tunable GMM kernels" which are simple and perform largely comparably
to tree methods on the same datasets. Note that "abc-robust-logitboost"
substantially improved the original "GDBT" in that (a) it developed a
tree-split formula based on second-order information of the derivatives of the
loss function; (b) it developed a new set of derivatives for multi-class
classification formulation.
  In the prior study in 2017, the "generalized min-max" (GMM) kernel was shown
to have good performance compared to the "radial-basis function" (RBF) kernel.
However, as demonstrated in this paper, the original GMM kernel is often not as
competitive as tree methods on the datasets used in the deep learning
literature. Since the original GMM kernel has no parameters, we propose tunable
GMM kernels by adding tuning parameters in various ways. Three basic (i.e.,
with only one parameter) GMM kernels are the "$e$GMM kernel", "$p$GMM kernel",
and "$\gamma$GMM kernel", respectively. Extensive experiments show that they
are able to produce good results for a large number of classification tasks.
Furthermore, the basic kernels can be combined to boost the performance.
