Online Estimation of Discrete Densities

Abstract—We address the problem of estimating a discrete joint density online, that is, the algorithm is only provided the current example and its current estimate. The proposed online estimator of discrete densities, EDDO (Estimation of Discrete Densities Online), uses classifier chains to model dependencies among features. Each classifier in the chain estimates the prob-ability of one particular feature. Because a single chain may not provide a reliable estimate, we also consider ensembles of classifier chains and ensembles of weighted classifier chains. For all density estimators, we provide consistency proofs and propose algorithms to perform certain inference tasks. The empirical evaluation of the estimators is conducted in several experiments and on data sets of up to several million instances: We compare them to density estimates computed from Bayesian structure learners, evaluate them under the influence of noise, measure their ability to deal with concept drift, and measure the run-time performance. Our experiments demonstrate that, even though designed to work online, EDDO delivers estimators of competitive accuracy compared to batch Bayesian structure learners and batch variants of EDDO. I