With the rapid growth of computer storage capacities, available data and demand for scoring models both follow an increasing trend, sharper than that of the processing power. However, the main limitation to a wide spread of data mining solutions is the non-increasing availability of skilled data analysts, which play a key role in data preparation and model selection. In this paper we present a parameter-free scalable classification method, which is a step towards fully automatic data mining. The method is based on Bayes optimal univariate conditional density estimators, naive Bayes classification enhanced with a Bayesian variable selection scheme, and averaging of models using a logarithmic smoothing of the posterior distribution. We focus on the complexity of the algorithms and show how they can cope with datasets that are far larger than the available central memory. We finally report results on the Large Scale Learning challenge, where our method obtains state of the art performance within practicable computation time.