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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Combinatorica 18 (1998), S. 151-171 
    ISSN: 1439-6912
    Keywords: AMS Subject Classification (1991) Classes:  60C05, 60E15, 68Q22, 68Q25, 68R10, 94C12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: We formulate the notion of a "good approximation" to a probability distribution over a finite abelian group ?. The quality of the approximating distribution is characterized by a parameter ɛ which is a bound on the difference between corresponding Fourier coefficients of the two distributions. It is also required that the sample space of the approximating distribution be of size polynomial in and 1/ɛ. Such approximations are useful in reducing or eliminating the use of randomness in certain randomized algorithms. We demonstrate the existence of such good approximations to arbitrary distributions. In the case of n random variables distributed uniformly and independently over the range , we provide an efficient construction of a good approximation. The approximation constructed has the property that any linear combination of the random variables (modulo d) has essentially the same behavior under the approximating distribution as it does under the uniform distribution over . Our analysis is based on Weil's character sum estimates. We apply this result to the construction of a non-binary linear code where the alphabet symbols appear almost uniformly in each non-zero code-word.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Data mining and knowledge discovery 2 (1998), S. 39-68 
    ISSN: 1573-756X
    Keywords: data mining ; market basket ; association rules ; dependence rules ; closure properties ; text mining
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract One of the more well-studied problems in data mining is the search for association rules in market basket data. Association rules are intended to identify patterns of the type: “A customer purchasing item A often also purchases item B.” Motivated partly by the goal of generalizing beyond market basket data and partly by the goal of ironing out some problems in the definition of association rules, we develop the notion of dependence rules that identify statistical dependence in both the presence and absence of items in itemsets. We propose measuring significance of dependence via the chi-squared test for independence from classical statistics. This leads to a measure that is upward-closed in the itemset lattice, enabling us to reduce the mining problem to the search for a border between dependent and independent itemsets in the lattice. We develop pruning strategies based on the closure property and thereby devise an efficient algorithm for discovering dependence rules. We demonstrate our algorithm's effectiveness by testing it on census data, text data (wherein we seek term dependence), and synthetic data.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Data mining and knowledge discovery 4 (2000), S. 163-192 
    ISSN: 1573-756X
    Keywords: data mining ; text mining ; market basket ; association rules ; causality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Mining for association rules in market basket data has proved a fruitful area of research. Measures such as conditional probability (confidence) and correlation have been used to infer rules of the form “the existence of item A implies the existence of item B.” However, such rules indicate only a statistical relationship between A and B. They do not specify the nature of the relationship: whether the presence of A causes the presence of B, or the converse, or some other attribute or phenomenon causes both to appear together. In applications, knowing such causal relationships is extremely useful for enhancing understanding and effecting change. While distinguishing causality from correlation is a truly difficult problem, recent work in statistics and Bayesian learning provide some avenues of attack. In these fields, the goal has generally been to learn complete causal models, which are essentially impossible to learn in large-scale data mining applications with a large number of variables. In this paper, we consider the problem of determining casual relationships, instead of mere associations, when mining market basket data. We identify some problems with the direct application of Bayesian learning ideas to mining large databases, concerning both the scalability of algorithms and the appropriateness of the statistical techniques, and introduce some initial ideas for dealing with these problems. We present experimental results from applying our algorithms on several large, real-world data sets. The results indicate that the approach proposed here is both computationally feasible and successful in identifying interesting causal structures. An interesting outcome is that it is perhaps easier to infer the lack of causality than to infer causality, information that is useful in preventing erroneous decision making.
    Type of Medium: Electronic Resource
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  • 4
    Book
    Book
    Cambridge u. :Cambridge University Press,
    Title: Randomized algorithms
    Author: Motwani, Rajeev
    Contributer: Raghavan, Prabhakar
    Publisher: Cambridge u. :Cambridge University Press,
    Year of publication: 1995
    Pages: 476 S.
    Series Statement: Stanford-Cambridge program
    Type of Medium: Book
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