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# Online Similarity Prediction of Networked Data from Known and Unknown Graphs

*Proceedings of the 26th Annual Conference on Learning Theory*, PMLR 30:662-695, 2013.

#### Abstract

We consider online similarity prediction problems over networked data. We begin by relating this task to the more standard class prediction problem, showing that, given an arbitrary algorithm for class prediction, we can construct an algorithm for similarity prediction with “nearly” the same mistake bound, and vice versa. After noticing that this general construction is computationally infeasible, we target our study to feasible similarity prediction algorithms on networked data. We initially assume that the network structure is known to the learner. Here we observe that Matrix Winnow (Warmuth, 2007) has a near-optimal mistake guarantee, at the price of cubic prediction time per round. This motivates our effort for an efficient implementation of a Perceptron-like algorithm with a weaker mistake guarantee but with only poly-logarithmic prediction time. Our focus then turns to the challenging case of networks whose structure is initially unknown to the learner. In this novel setting, where the network structure is only incrementally revealed, we obtain a mistake-bounded algorithm with a quadratic prediction time per round.