Traditional machine learning methods only consider relationships between feature values within individual data instances while disregarding the dependencies that link features across instances. In this work, we develop a general approach to supervised learning by leveraging higher-order dependencies between features. We introduce a novel Bayesian framework for classification named Higher Order Naive Bayes (HONB). Unlike approaches that assume data instances are independent, HONB leverages co-occurrence relations between feature values across different instances. Additionally, we generalize our framework by developing a novel data-driven space transformation that allows any classifier operating in vector spaces to take advantage of these higher-order co-occurrence relations. Results obtained on several benchmark text corpora demonstrate that higher-order approaches achieve significant improvements in classification accuracy over the baseline (first-order) methods.