Abstract |
We give an online algorithm and prove novel mistake and regret bounds for online binary matrix completion with side information. The mistake bounds we prove SVM (perceptron) bounds. More specifically, if we assume that there is some factorization of the underlying m ⇥ n matrix into P Q> , where the rows of P are interpreted as “classifiers” in <d and the rows of Q as “instances” in <d, then � is isthemaximum(normalized)marginoverallfactorizationsPQ> consistentwith the observed matrix. The quasi-dimension term D measures the quality of side information. In the presence of vacuous side information, D = m + n. However, if the side information is predictive of the underlying factorization of the matrix, then in an ideal case, D 2 O(k + `) where k is the number of distinct row factors and ` is the number of distinct column factors. We additionally provide a generalization of our algorithm to the inductive setting. In this setting, we provide an example where the side information is not directly specified in advance. For this example, the quasi-dimension D is now bounded by O(k2 + `2). |