  This paper provides elementary analyses of the regret and generalization of
minimum-norm interpolating classifiers (MNIC). The MNIC is the function of
smallest Reproducing Kernel Hilbert Space norm that perfectly interpolates a
label pattern on a finite data set. We derive a mistake bound for MNIC and a
regularized variant that holds for all data sets. This bound follows from
elementary properties of matrix inverses. Under the assumption that the data is
independently and identically distributed, the mistake bound implies that MNIC
generalizes at a rate proportional to the norm of the interpolating solution
and inversely proportional to the number of data points. This rate matches
similar rates derived for margin classifiers and perceptrons. We derive several
plausible generative models where the norm of the interpolating classifier is
bounded or grows at a rate sublinear in $n$. We also show that as long as the
population class conditional distributions are sufficiently separable in total
variation, then MNIC generalizes with a fast rate.
