In this paper we present a simple to implement truly online large margin version of the Perceptron ranking (PRank) algorithm, called the OAP-BPM (Online Aggregate Prank-Bayes Point Machine) algorithm, which finds a rule that correctly ranks a given training sequence of instance and target rank pairs. PRank maintains a weight vector and a set of thresholds to define a ranking rule that maps each instance to its respective rank. The OAP-BPM algorithm is an extension of this algorithm by approximating the Bayes point, thus giving a good generalization performance. The Bayes point is approximated by averaging the weights and thresholds associated with several PRank algorithms run in parallel. In order to ensure diversity amongst the solutions of the PRank algorithms we randomly subsample the stream of incoming training examples. We also introduce two new online versions of Bagging and the voted Perceptron using the same randomization trick as OAP-BPM, hence are referred to as OAP with extension -Bagg and -VP respectively. A rank learning experiment was conducted on a synthetic data set and collaborative filtering experiments on a number of real world data sets were conducted, showing that OAP-BPM has a better performance compared to PRank and a pure online regression algorithm, albeit with a higher computational cost, though is not too prohibitive.

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