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The likelihood for patterns of continuous attributes for the naive Bayesian classifier (NBC) may be approximated by kernel density estimation (KDE), letting every pattern influence the shape of the probability density, thus leading to accurate estimation. KDE suffers from computational cost, making it unpractical in many real-world applications. We smooth the density using a spline, thus requiring only very few coefficients for the estimation rather than the whole training set, allowing rapid implementation of the NBC without sacrificing classifier accuracy. Experiments conducted over several real-world databases reveal acceleration, sometimes in several orders of magnitude, in favor of the spline approximation, making the application of KDE to the NBC practical.