Prediction is an important component in a variety of domains in Artificial Intelligence and Machine Learning, in order that Intelligent Systems may make more informed and reliable decisions. Certain domains require that prediction be performed on sequences of events that can typically be modeled as stochastic processes. This work presents Active LeZi, a sequential prediction algorithm that is founded on an Information Theoretic approach, and is based on the acclaimed LZ78 family of data compression algorithms. The efficacy of this algorithm in a typical Smart Environment - the Smart Home, is demonstrated by employing this algorithm to predict device usage in the home. The performance of this algorithm is tested on synthetic data sets that are representative of typical interactions between a Smart Home and the inhabitant.
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