Authors have performed learning algorithms, based on mixtures of experts, who achieve a good performance under severe time/cost restrictions, and that can be applied to non-stationary data. This is of particular interest for applications like quality of Service (QoS) prediction on IP data networks (see [12]). In this paper we show how can all the properties of this algorithms be proved in a strictly rigorous manner, with no other tools that elementary martingale theory at hand
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