Block-Coordinate Frank-Wolfe Optimization for Structural SVMs

We propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full Frank-Wolfe algorithm. We also show that, when applied to the dual structural support vector machine (SVM) objective, this yields an online algorithm that has the same low iteration complexity as primal stochastic subgradient methods. However, unlike stochastic subgradient methods, the block-coordinate Frank-Wolfe algorithm allows us to compute the optimal step-size and yields a computable duality gap guarantee. Our experiments indicate that this simple algorithm outperforms competing structural SVM solvers.Comment: Appears in Proceedings of the 30th International Conference on Machine Learning (ICML 2013). 9 pages main text + 22 pages appendix. Changes from v3 to v4: 1) Re-organized appendix; improved & clarified duality gap proofs; re-drew all plots; 2) Changed convention for Cf definition; 3) Added weighted averaging experiments + convergence results; 4) Clarified main text and relationship with appendi

Spanning tree approximations for conditional random fields

Abstract In this work we show that one can train Conditional Random Fields of intractable graphs effectively and efficiently by considering a mixture of random spanning trees of the underlying graphical model. Furthermore, we show how a maximum-likelihood estimator of such a training objective can subsequently be used for prediction on the full graph. We present experimental results which improve on the state-of-the-art. Additionally, the training objective is less sensitive to the regularization than pseudo-likelihood based training approaches. We perform the experimental validation on two classes of data sets where structure is important: image denoising and multilabel classification