We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear separators. We consider both the malicious noise model of Valiant [Valiant 1985; Kearns and Li 1988] and the adversarial label noise model of Kearns, Schapire, an...

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In sparse Cholesky factorization, nding elimination orderings that produce small ll-in is very important and various heuristics have been proposed. For parallel computations, good orderings should produce elimination trees of low height. Finding optimal ll-in orderings and nding optimal height orderings are NP-hard problems. A class of Nested Dissection orderings with minimal separators, has be...

In this paper we describe a top-down approach to the segmentation and representation of documents containing tabular structures. Examples of these documents are invoices and technical papers with tables. The segmentation is based on an extension of X-Y trees, where the regions are split by means of cuts along separators (e.g. lines), in addition to cuts along white spaces. The leaves describe r...

We provide a minimal counterexample to the correctness of an algorithm proposed by R. Tarjan for decomposing a graph by maximal clique separators. We also suggest a modification to that algorithm which not only corrects it but also retains its O(nm) time complexity.

We define a novel, basic, unsupervised learning problem learning the lowest density homogeneous hyperplane separator of an unknown probability distribution. This task is relevant to several problems in machine learning, such as semi-supervised learning and clustering stability. We investigate the question of existence of a universally consistent algorithm for this problem. We propose two natura...