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Propositional and relational Bayesian networks associated with imprecise and qualitative probabilistic assessments
 IN PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 2004
"... This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and firstorder constructs together with precise, imprecise, indeterminate and qualitative probabilistic as ..."
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Cited by 10 (6 self)
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This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and firstorder constructs together with precise, imprecise, indeterminate and qualitative probabilistic assessments. The paper shows how this can be achieved through the theory of credal networks. New exact and approximate inference algorithms based on multilinear programming and iterated/loopy propagation of interval probabilities are presented; their superior performance, compared to existing ones, is shown empirically.
Itemset Frequency Satisfiability: Complexity and Axiomatization
, 2007
"... Computing frequent itemsets is one of the most prominent problems in data mining. We study the following related problem, called FREQSAT, in depth: given some itemsetinterval pairs, does there exist a database such that for every pair the frequency of the itemset falls into the interval? This probl ..."
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Cited by 3 (1 self)
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Computing frequent itemsets is one of the most prominent problems in data mining. We study the following related problem, called FREQSAT, in depth: given some itemsetinterval pairs, does there exist a database such that for every pair the frequency of the itemset falls into the interval? This problem is shown to be NPcomplete. The problem is then further extended to include arbitrary Boolean expressions over items and conditional frequency expressions in the form of association rules. We also show that, unless P equals NP, the related function problem—find the best interval for an itemset under some frequency constraints—cannot be approximated efficiently. Furthermore, it is shown that FREQSAT is recursively axiomatizable, but that there cannot exist an axiomatization of finite arity.
The Complexity of Satisfying Constraints on Databases of Transactions
"... Abstract Computing frequent itemsets is one of the most prominent problems in data mining. Recently, a new related problem, called FREQSAT, was introduced and studied: given some itemsetinterval pairs, does there exist a database such that for every pair, the frequency of the itemset falls in the i ..."
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Cited by 2 (0 self)
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Abstract Computing frequent itemsets is one of the most prominent problems in data mining. Recently, a new related problem, called FREQSAT, was introduced and studied: given some itemsetinterval pairs, does there exist a database such that for every pair, the frequency of the itemset falls in the interval? In this paper, we extend this FREQSATproblem by further constraining the database by giving other characteristics as part of the input as well. These characteristics are the maximal transaction length, the maximal number of transactions, and the maximal number of duplicates of a transaction. These extensions and all their combinations are studied in depth, and a hierarchy w.r.t. complexity is given. To make a complete picture, also the cases where the characteristics are constant; i.e., bounded and the bound being a fixed constant that is not a part of the input, are studied. 1
Itemset Frequency Satisfiability: Complexity and Axiomatization 1
"... Computing frequent itemsets is one of the most prominent problems in data mining. We study the following related problem, called FREQSAT, in depth: given some itemsetinterval pairs, does there exist a database such that for every pair the frequency of the itemset falls into the interval? This probl ..."
Abstract
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Computing frequent itemsets is one of the most prominent problems in data mining. We study the following related problem, called FREQSAT, in depth: given some itemsetinterval pairs, does there exist a database such that for every pair the frequency of the itemset falls into the interval? This problem is shown to be NPcomplete. The problem is then further extended to include arbitrary Boolean expressions over items and conditional frequency expressions in the form of association rules. We also show that, unless P equals NP, the related function problem—find the best interval for an itemset under some frequency constraints—cannot be approximated efficiently. Furthermore, it is shown that FREQSAT is recursively axiomatizable, but that there cannot exist an axiomatization of finite arity.