This article studies the task of discovering correspondences across related domains based on real-world data collections. We address this task through a designated extension of distributional data-clustering methods. The method is empirically demonstrated on synthetic data as well as on texts addressing different religions, where the goal is to identify commonalities shared by all religions. This article generalises and demonstrates the empirical improvement relative to our previous studies on this subject, as well as to other comparable methods.

We propose an information-theoretic clustering approach that incorporates a pre-known partition of the data, aiming to identify common clusters that cut across the given partition. In the standard clustering setting the formation of clusters is guided by a single source of feature information. The newly utilized pre-partition factor introduces an additional bias that counterbalances the impact of the features whenever they become correlated with this known partition. The resulting algorithmic framework was applied successfully to synthetic data, as well as to identifying text-based cross-religion correspondences.

In this paper, we prove various results about PAC learning in the presence of malicious noise. Our main interest is the sample size behavior of learning algorithms. We prove the first nontrivial sample complexity lower bound in this model by showing that order of ε/Δ 2 + d /Δ (up to logarithmic factors) examples are necessary for PAC learning any target class of {0,1}-valued functions of VC dimension d , where ε is the desired accuracy and η = ε/(1 + ε) - Δ the malicious noise rate (it is well known that any nontrivial target class cannot be PAC learned with accuracy ε and malicious noise rate η ≥ ε/(1 + ε), this irrespective to sample complexity). We also show that this result cannot be significantly improved in general by presenting efficient learning algorithms for the class of all subsets of d elements and the class of unions of at most d intervals on the real line. This is especialy interesting as we can also show that the popular minimum disagreement strategy needs samples of size d ε/Δ 2 , hence is not optimal with respect to sample size. We then discuss the use of randomized hypotheses. For these the bound ε/(1 + ε) on the noise rate is no longer true and is replaced by 2ε/(1 + 2ε). In fact, we present a generic algorithm using randomized hypotheses that can tolerate noise rates slightly larger than ε/(1 + ε) while using samples of size d /ε as in the noise-free case. Again one observes a quadratic powerlaw (in this case d ε/Δ 2 , Δ = 2ε/(1 + 2ε) - η) as Δ goes to zero. We show upper and lower bounds of this order.

Article Finding hidden Hamiltonian cycles Share on Authors: Andrei Z. Broder DEC Systems Research Center, Palo Alto, CA DEC Systems Research Center, Palo Alto, CAView Profile , Alan M. Frieze Carnegie-Mellon Univ., Pittsburgh, PA Carnegie-Mellon Univ., Pittsburgh, PAView Profile , Eli Shamir Hebrew Univ., Jerusalem, Israel Hebrew Univ., Jerusalem, IsraelView Profile Authors Info & Claims STOC '91: Proceedings of the twenty-third annual ACM symposium on Theory of ComputingJanuary 1991 Pages 182–189https://doi.org/10.1145/103418.103442Online:03 January 1991Publication History 11citation341DownloadsMetricsTotal Citations11Total Downloads341Last 12 Months2Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Expanders have many applications in Computer Science. It is known that random d-regular graphs are very efficient expanders, almost surely. However, checking whether a particular graph is a good expander is co-NP-complete. We show that the second eigenvalue of d-regular graphs, λ2, is concentrated in an interval of width O(√d) around its mean, and that its mean is O(d3/4). The result holds under various models for random d-regular graphs. As a consequence a random d-regular graph on n vertices, is, with high probability a certifiable efficient expander for n sufficiently large. The bound on the width of the interval is derived from martingale theory and the bound on E(λ2) is obtained by exploring the properties of random walks in random graphs.

A perfect matching in a graph G(V,E), also called a 1-factor, is a collection P of non-interesting edges engaging (incident with) all the vertices; in case G is bipartite V = M @@@@ F, M @@@@ F = φ, P should engage all the vertices of M. The combinatorial problem of finding a perfect matching in G (and its rich ramifications) were extensively studied (and applied) from existential, algorithmic and probabilistic points of view.

A simple property of number representations yields a unit cross section relation between points and interval representations. Applied to product regions in a vector space, one obtains simple, practical and flexible algorithms for dynamic range search and related queries.

A bound for the number of steps that are required to evaluate Boolean expressions is obtained. It is shown that any Boolean expression of n distinct variables may be evaluated in $2\log _2 n - 1$ steps if sufficiently many processors are available.

A definite automaton is, roughly speaking, an automaton (sequential circuit) with the property that for some fixed integer k its action depends only on the last k inputs. The notion of a definite event introduced by Kleene, as well as the related concepts of definite automata and tables, are studied here in detail. Basic results relating to the minimum number of states required for synthesizing an automaton of a given degree of definiteness are proved. We give a characterization of all k-definite events definable by k+1 state automata. Various decision problems pertaining to definite automata are effectively solved. We also solve effectively the problem of synthesizing a minimal automaton defining a given definite event. The solutions of decision and synthesis problems given here are practical in the sense that if the problem is presented by n units of information, then the algorithm in question requires about n3 steps of a very elementary nature (rather than requiring about 2n steps as some algorithms for automata do, which puts them beyond the capacity of the largest computers even for relatively small values of n). A notion of equivalence of definite events is introduced and the uniqueness of the minimal automaton defining an event in an equivalence class is proved.