Universal Algorithms for Probability Forecasting

Multi-class classification is one of the most important tasks in machine learning. In this paper we consider two online multi-class classification problems: classification by a linear model and by a kernelized model. The quality of predictions is measured by the Brier loss function. We obtain two computationally efficient algorithms for these problems by applying the Aggregating Algorithms to certain pools of experts and prove theoretical guarantees on the losses of these algorithms.We kernelize one of the algorithms and prove theoretical guarantees on its loss. We perform experiments and compare our algorithms with logistic regression.