Nonparametric Estimation and On-Line Prediction for General Stationary Ergodic Sources

We propose a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. The idea is to prapare many histograms and estimate the probability distribution of the bins in each histogarm. We do not know a priori which histogram expresses the true distribution: if the histogram is too sharp, the estimation captures the noise too much (overestimation). To this end, we weight those distributions to obtain the estimation of the true distribution. As long as the weights are positive, we obtain a desired property: the Kullback-Leiber information divided by the number n of examples diminishes as n grows.