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.

Today's deep neural networks perform incredible feats when provided sufficient training data. Sadly, annotating enough raw data to train your favorite classifier can often be prohibitively expensive, especially in important scenarios like computer-assisted medical diagnoses where labeling requires the advice of human experts. This issue has led to a surge of interest in active learning, a paradigm introduced to mitigate extravagant labeling costs. Active learning, originally studied by Angluin in 1988 [1], is in essence formed around two basic hypotheses: raw (unlabeled) data is cheap, and not all data is equally useful. The idea is that by adaptively selecting only the most informative data to label, we can get the same accuracy without the prohibitive cost.

Location estimation is one of the most basic questions in parametric statistics. Suppose we have a known distribution density f, and we get n i.i.d.