Regularized Frank-Wolfe for Dense CRFs: Generalizing Mean Field and Beyond

International audienceWe introduce regularized Frank-Wolfe, a general and effective algorithm for inference and learning of dense conditional random fields (CRFs). The algorithm optimizes a nonconvex continuous relaxation of the CRF inference problem using vanilla Frank-Wolfe with approximate updates, which are equivalent to minimizing a regularized energy function. Our proposed method is a generalization of existing algorithms such as mean field or concave-convex procedure. This perspective not only offers a unified analysis of these algorithms, but also allows an easy way of exploring different variants that potentially yield better performance. We illustrate this in our empirical results on standard semantic segmentation datasets, where several instantiations of our regularized Frank-Wolfe outperform mean field inference, both as a standalone component and as an end-to-end trainable layer in a neural network. We also show that dense CRFs, coupled with our new algorithms, produce significant improvements over strong CNN baselines

SDCA-Powered Inexact Dual Augmented Lagrangian Method for Fast CRF Learning

International audienceWe propose an efficient dual augmented La-grangian formulation to learn conditional random fields (CRF). Our algorithm, which can be interpreted as an inexact gradient descent algorithm on the multiplier, does not require to perform global inference iteratively, and requires only a fixed number of stochastic clique-wise updates at each epoch to obtain a sufficiently good estimate of the gradient w.r.t. the Lagrange multipliers. We prove that the proposed algorithm enjoys global linear convergence for both the primal and the dual objectives. Our experiments show that the proposed algorithm outperforms state-of-the-art baselines in terms of speed of convergence