We investigate the problem of sequentially selecting elements of an unknown matroid in an online manner to form an independent set, with the goal of maximizing the minimum probability of acceptance across all elements, a property we define as f-fairness. Under adversarial arrival orders, we design an α(lnk + 1)-fair algorithm, where α is the arboricity of the matroid and k is the rank, a result that is nearly optimal. For laminar matroids, we develop a (2α 1)-fair algorithm, which is optimal up to constant factors, achieved through a novel online coloring scheme. In the random arrival order setting, we achieve a (4+o(1))α-fair algorithm for graphic matroids, matching the optimal result up to constant factors, relying on a novel technique for learning a degeneracy ordering using a sampled subset of edges. We further generalize our result to p-matchoids, obtaining a β(plnk + 1)-fair algorithm for the adversarial arrival model, where β is the optimal offline fairness. Notably, all our results can be extended to a setting with no prior knowledge of the matroid with only a logarithmic increase in the fairness factor.

Recent years have revealed an unprecedented demand for AI-based technology, leading to a common setting where immense data is distributed across multiple locations. This creates a communication bottleneck among the storage facilities, often aiming to jointly solve tasks of small solution size k from input of astronomically large size n. Motivated by federated and distributed machine learning applications, we study two fundamental optimization problems, maximum weight matroid independent set (MW-IS) and maximum weight matching (MWM), in a zero communication computational model. In this model, the data is dispersed between m servers. Without any communication, each server has to send a message to a central coordinator which is required to compute an optimal solution for the original (large) instance.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Thus, weaker models that give imprecise results quickly can be advantageous, provided inaccuracies can be resolved using few queries to a stronger model. In the fundamental problem of computing a maximum-weight basis of a matroid, a well-known generalization of many combinatorial optimization problems, algorithms have access to a clean oracle to query matroid information. We additionally equip algorithms with a fast but dirty oracle. We design and analyze practical algorithms that only use few clean queries w.r.t. the quality of the dirty oracle, while maintaining robustness against arbitrarily poor dirty oracles, approaching the performance of classic algorithms for the given problem. Notably, we prove that our algorithms are, in many respects, best-possible. Further, we outline extensions to other matroid oracle types, non-free dirty oracles and other matroid problems.

In our case, it boils down to: ' The smoothing effect induced by the average helps to reduce the visual noise, and hence improves the explanations. For the experiment, m and are the same as SmoothGrad. We start by deriving the closed form of Saliency (SA) and naturally Gradient-Input (GI): ' The case of V arGrad is specific, as the gradient of a linear system being constant, its variance is null. W We recall that for Gradient Input, Integrated Gradients, Occlusion, ' It was quickly realized that they unified properties of various domains such as graph theory, linear algebra or geometry. Later, in the '60s, a connection was made At each step, the insertion metric selects the concepts of maximum score given a cardinality constraint.

Neural Information Processing Systems http://nips.cc/