We present a new multivariate event classifier, the PDE classifier, wh
ich can be used to identify rare signals in the presence of large back
grounds. The classifier is based on a discriminant function which uses
kernel density estimates of the signal and background event densities
. The PDE method offers the flexibility of a neural network but is con
ceptually simpler, theoretically better understood, and easier to opti
mize in practice. The technique is tested on Monte Carlo data using pr
ocesses t ($) over bar t --> e + E(t) + jets as signal and W + jets --
> e + E(t) + jets as background. The performance of the PDE classifier
is similar to that of a neural network. Both methods outperform conve
ntional analysis.