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We revisit the elegant observation of T. Cover '65 which, perhaps, is not aswell-known to the broader community as it should be. The first goal of thetutorial is to explain---through the prism of this elementary result---how tosolve certain sequence prediction problems by modeling sets of solutions ratherthan the unknown data-generating mechanism. We extend Cover's observation inseveral directions and focus on computational aspects of the proposedalgorithms. The applicability of the methods is illustrated on severalexamples, including node classification in a network.  The second aim of this tutorial is to demonstrate the following phenomenon:it is possible to predict as well as a combinatorial "benchmark" for which wehave a certain multiplicative approximation algorithm, even if the exactcomputation of the benchmark given all the data is NP-hard. The proposedprediction methods, therefore, circumvent some of the computationaldifficulties associated with finding the best model given the data. Thesedifficulties arise rather quickly when one attempts to develop a probabilisticmodel for graph-based or other problems with a combinatorial structure.

A Tutorial on Online Supervised Learning with Applications to Node Classification in Social Networks