5 accepted papers
We introduce a new framework for the exact point-wise ℓp robustness verification problem that exploits the layer-wise geometric structure of deep feed-forward networks with rectified linear activations (ReLU networks). The activation regions of the network partition the input space, and one can veri…
We study a generalization of the classic isotonic regression problem where we allow separable nonconvex objective functions, focusing on the case of estimators used in robust regression. A simple dynamic programming approach allows us to solve this problem to within ε-accuracy (of the global minimu…
The k-support and OWL norms generalize the l1 norm, providing better prediction accuracy and better handling of correlated variables. We study the norms obtained from extending the k-support norm and OWL norms to the setting in which there are overlapping groups. The resulting norms are in general N…
We describe the use of sorting networks to form relaxations of problems involving permutations of n objects. This approach is an alternative to relaxations based on the Birkhoff polytope (the set of n \times n doubly stochastic matrices), providing a more compact formulation in which the only constr…
The problem of projecting onto the permutahedron \mathbfPH(c) – the convex hull of all permutations of a fixed vector c – under a uniformly separable Bregman divergence is shown to be reducible to the Isotonic Optimization problem. This allows us to employ known fast algorithms to improve on several…