The paper proposes the vicinities merging algorithm for prediction with side information. The algorithm is based on specialist experts techniques. We use vicinities in the side information domain to identify relevant past examples, apply standard learning techniques to them, and then use prediction with expert advice tools to merge those predictions. Guarantees from the theory of prediction with expert advice ensure that helpful vicinities are selected dynamically. The algorithm automatically converges on the right vicinities from an initial broad selection. We apply the resulting algorithms to two problems, prediction of implied volatility of options and prediction of students' performance at tests. On the problem of predicting implied volatility, the algorithm consistently outperforms naive competitors and a highly-tuned proprietary method used in the industry. When applied to the students' performance, the algorithm never falls behind the baseline and outperforms it when the side information is beneficial.