  We propose a probabilistic enhancement of standard kernel Support Vector
Machines for binary classification, in order to address the case when, along
with given data sets, a description of uncertainty (e.g., error bounds) may be
available on each datum. In the present paper, we specifically consider
Gaussian distributions to model uncertainty. Thereby, our data consist of pairs
$(x_i,\Sigma_i)$, $i\in\{1,\ldots,N\}$, along with an indicator
$y_i\in\{-1,1\}$ to declare membership in one of two categories for each pair.
These pairs may be viewed to represent the mean and covariance, respectively,
of random vectors $\xi_i$ taking values in a suitable linear space (typically
$\mathbb R^n$). Thus, our setting may also be viewed as a modification of
Support Vector Machines to classify distributions, albeit, at present, only
Gaussian ones. We outline the formalism that allows computing suitable
classifiers via a natural modification of the standard "kernel trick." The main
contribution of this work is to point out a suitable kernel function for
applying Support Vector techniques to the setting of uncertain data for which a
detailed uncertainty description is also available (herein, "Gaussian points").
