  We define a violator operator which captures the definition of a minimal
Gr\"obner basis of an ideal. This construction places the problem of computing
a Gr\"obner basis within the framework of violator spaces, introduced in 2008
by G{\"a}rtner, Matou{\v{s}}ek, R{\"u}st, and {\v{S}}kovro{\v{n}} in a
different context. The key aspect which we use is their successful utilization
of a Clarkson-style fast sampling algorithm from geometric optimization. Using
the output of a machine learning algorithm, we combine the prediction of the
size of a minimal Gr\"obner basis of an ideal with the Clarkson-style biased
random sampling method to compute a Gr\"obner basis in expected runtime linear
in the size of the violator space.
