Modeling and prediction of temporal sequences is central to many signal processing and machine learning applications. Prediction based on sequence history is typically performed using parametric models, such as fixed-order Markov chains ($n$-grams), approximations of high-order Markov processes, such as mixed-order Markov models or mixtures of lagged bigram models, or with other machine learning techniques. This paper presents a method for sequence prediction based on sparse hyperdimensional coding of the sequence structure and describes how higher order temporal structures can be utilized in sparse coding in a balanced manner. The method is purely incremental, allowing real-time online learning and prediction with limited computational resources.

Experiments with prediction of mobile phone use patterns, including the prediction of the next launched application, the next GPS location of the user, and the next artist played with the phone media player, reveal that the proposed method is able to capture the relevant variable-order structure from the sequences. In comparison with the n-grams and the mixed-order Markov models, the sparse hyperdimensional predictor clearly outperforms its peers in terms of unweighted average recall and achieves an equal level of weighted average recall as the mixed-order Markov chain but without the batch training of the mixed-order model.

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