The concept of matching dependencies (mds) is recently pro- posed for specifying matching rules for object identification. Similar to the functional dependencies (with conditions), mds can also be applied to various data quality applications such as violation detection. In this paper, we study the problem of discovering matching dependencies from a given database instance. First, we formally define the measures, support and confidence, for evaluating utility of mds in the given database instance. Then, we study the discovery of mds with certain utility requirements of support and confidence. Exact algorithms are developed, together with pruning strategies to improve the time performance. Since the exact algorithm has to traverse all the data during the computation, we propose an approximate solution which only use some of the data. A bound of relative errors introduced by the approximation is also developed. Finally, our experimental evaluation demonstrates the efficiency of the proposed methods.
The confidence and support measures are widely used in discovering approximate functional dependencies @cite_15 @cite_26 and evaluating @cite_12 @cite_3 @cite_17 . The confidence can be interpreted as an estimate of the probability that a randomly drawn pair of tuples agreeing on @math also agree on @math @cite_22 @cite_14 . Scheffer @cite_4 study the trade off between support and confidence for finding association rules @cite_19 , by computing a expected prediction accuracy. In addition, Chiang and Miller @cite_3 also study some other measures such as conviction and @math -test for evaluating dependency rules. When a candidate @math is suggested together with minimum support and confidence, @cite_12 study the discovery of optimal with the minimum pattern tableau size. A concise set of patterns are naturally desirable which may have lower cost during the applications such as violation detection by . On the other hand, Chiang and Miller @cite_3 explore by considering all the possible dependency candidates when @math is not specified. @cite_17 , also study the case when the embedded are not given, and propose three algorithms for different scenarios.
@cite_26 @cite_14 @cite_22 @cite_4 @cite_3 @cite_19 @cite_15 @cite_12 @cite_17
2000931246 2169388387 2066277072 1994962776
Let f be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number k such that if the ratio of the number of clauses over the number of variables of f strictly exceeds k , then f is almost certainly unsatisfiable. By a well-known and more or less straightforward argument, it can be shown that kF5.191. This upper bound was improved by to 4.758 by first providing new improved bounds for the occupancy problem. There is strong experimental evidence that the value of k is around 4.2. In this work, we define, in terms of the random formula f, a decreasing sequence of random variables such that, if the expected value of any one of them converges to zero, then f is almost certainly unsatisfiable. By letting the expected value of the first term of the sequence converge to zero, we obtain, by simple and elementary computations, an upper bound for k equal to 4.667. From the expected value of the second term of the sequence, we get the value 4.601q . In general, by letting the U This work was performed while the first author was visiting the School of Computer Science, Carleton Ž University, and was partially supported by NSERC Natural Sciences and Engineering Research Council . of Canada , and by a grant from the University of Patras for sabbatical leaves. The second and third Ž authors were supported in part by grants from NSERC Natural Sciences and Engineering Research . Council of Canada . During the last stages of this research, the first and last authors were also partially Ž . supported by EU ESPRIT Long-Term Research Project ALCOM-IT Project No. 20244 . †An extended abstract of this paper was published in the Proceedings of the Fourth Annual European Ž Symposium on Algorithms, ESA’96, September 25]27, 1996, Barcelona, Spain Springer-Verlag, LNCS, . pp. 27]38 . That extended abstract was coauthored by the first three authors of the present paper. Correspondence to: L. M. Kirousis Q 1998 John Wiley & Sons, Inc. CCC 1042-9832r98r030253-17 253 Determining the structure of dependencies among a set of variables is a common task in many signal and image processing applications, including multitarget tracking and computer vision. In this paper, we present an information-theoretic, machine learning approach to problems of this type. We cast this problem as a hypothesis test between factorizations of variables into mutually independent subsets. We show that the likelihood ratio can be written as sums of two sets of Kullback-Leibler (KL) divergence terms. The first set captures the structure of the statistical dependencies within each hypothesis, whereas the second set measures the details of model differences between hypotheses. We then consider the case when the signal prior models are unknown, so that the distributions of interest must be estimated directly from data, showing that the second set of terms is (asymptotically) negligible and quantifying the loss in hypothesis separability when the models are completely unknown. We demonstrate the utility of nonparametric estimation methods for such problems, providing a general framework for determining and distinguishing between dependency structures in highly uncertain environments. Additionally, we develop a machine learning approach for estimating lower bounds on KL divergence and mutual information from samples of high-dimensional random variables for which direct density estimation is infeasible. We present empirical results in the context of three prototypical applications: association of signals generated by sources possessing harmonic behavior, scene correspondence using video imagery, and detection of coherent behavior among sets of moving objects. Many techniques for association rule mining and feature selection require a suitable metric to capture the dependencies among variables in a data set. For example, metrics such as support, confidence, lift, correlation, and collective strength are often used to determine the interestingness of association patterns. However, many such measures provide conflicting information about the interestingness of a pattern, and the best metric to use for a given application domain is rarely known. In this paper, we present an overview of various measures proposed in the statistics, machine learning and data mining literature. We describe several key properties one should examine in order to select the right measure for a given application domain. A comparative study of these properties is made using twenty one of the existing measures. We show that each measure has different properties which make them useful for some application domains, but not for others. We also present two scenarios in which most of the existing measures agree with each other, namely, support-based pruning and table standardization. Finally, we present an algorithm to select a small set of tables such that an expert can select a desirable measure by looking at just this small set of tables. The functional dependency inference problem is the following. Given a relation r, find a set of functional dependencies that is equivalent with the set of all functional dependencies holding in r. All known algorithms for this task have running times that can be in the worst case exponential in the size of the smallest cover of the dependency set. We consider approximate dependency inference. We define various measures for the error of a dependency in a relation. These error measures have the value 0 if the dependency holds and a value close to 1 if the dependency clearly does not hold. Depending on the measure used, all dependencies with error at least e in r can be detected with high probability by considering only O(1 e) or O(|r| 1 2 e) random tuples of r. We also show how a machine learning algorithm due to can be applied to give in output-polynomial time an approximately correct cover for the set of dependencies holding in r.