Efficient Feature Group Sequencing for Anytime Linear Prediction

We propose a regularized linear learning algorithm to sequence groups of features, where each group incurs test-time cost or computation. Specifically, we develop a simple extension to Orthogonal Matching Pursuit (OMP) that respects the structure of groups of features with variable costs, and we prove that it achieves near-optimal anytime linear prediction at each budget threshold where a new group is selected. Our algorithm and analysis extends to generalized linear models with multi-dimensional responses. We demonstrate the scalability of the resulting approach on large real-world data-sets with many feature groups associated with test-time computational costs. Our method improves over Group Lasso and Group OMP in the anytime performance of linear predictions, measured in timeliness, an anytime prediction performance metric, while providing rigorous performance guarantees.