Mixture of Vector Experts
We describe and analyze an algorithm for predicting a sequence of n-dimensional binary vectors based on a set of experts making vector predictions in [0,1]^n. We measure the loss of individual predictions by the 2-norm between the actual outcome vector and the prediction. The loss of an expert is then the sum of the losses experienced on individual trials. We obtain bounds for the loss of our expert algorithm in terms of the loss of the best expert analogous to the well-known results for scalar experts making real-valued predictions of a binary outcome.