Webb, G. I. (1995). OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 5, 431--465.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....specify a different minimum item support for each item. Different rules may need to satisfy different minimum supports, depending on what items are in the rules. Besides the measures we have mentioned, some other measures for a rule include gain [FMM 96] entropy gain [MFM 98, Mor98] and laplace [CB91, Web95]. 2.9. Derive High Confidence Rules In some situations, users are interested in finding rules with high confidence but not necessarily high support. The algorithms we discussed before, such as Apriori, cannot handle this problem because they are support based algorithms. There are some studies ....

G. I. Webb, "OPUS: An Efficient Admissible Algorithm for Unordered Search," Journal of Artificial Intelligence Research, Vol. 3, 1995, pp. 431465. 136

....found to be large in the previous pass. This has the effect of pruning the search because any subset of a large itemset is also likely to be large [29] 2.4.3. 3 OPUS AR OPUS AR [27] is an algorithm for association rule analysis based on the efficient Optimised Pruning for Unordered Search (OPUS) [35] search algorithm. When compared with Apriori [29] OPUS AR requires more passes though the dataset. However, if the data can be retained in memory, this is not such a problem [27] 15 A commercial implementation of the OPUS AR algorithm, called Magnum Opus [36] was used in these experiments. ....

....associations between numeric variables impact rules. Later it was suggested they be called impact rules [32] to avoid confusion with other research. OPUS IR [32] is an efficient algorithm for discovery of impact rules using the based on the efficient Optimised Pruning for Unordered Search (OPUS) [35] search algorithm. 16 2.5 Contrast sets Contrast sets [13, 14] can be used to identify differences between groups. Contrastsets are defined as conjunctions of attributes value pairs that differ meaningfully in their probabilities across several groups. 2.5.1 STUCCO algorithm STUCCO (Search and ....

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Webb, G.I., OPUS: An Efficient Admissible Algorithm for Unordered Search. Journal of Artificial Intelligence Research, 1995. 3: p. 431-465.

....of patterns in the streams. finds the k strongest dependencies in a set of streams by performing a systematic searchover the space of all possible dependencies. Systematic search expands the children of search nodes in a manner that ensures that no node can ever be generated more than once [9 12, 14]. Because non redundant expansion is achieved without access to large, rapidly changing data structures, such as lists of open and closed nodes, the search space can be divided between multiple processes on multiple machines. Only a small amount of inter process communication is required to keep ....

....of streams is systematic, leading to search efficiency and parallelizability. Systematic searchnonredundantly enumerates the elements of search spaces for which the value or semantics of any given node are independent of the path from the root to that node. Webb calls such search spaces unordered [14]. Consider the space of disjunctive concepts over the set of literals fA# B# Cg. Given a root node containing the empty disjunct, false, and a set of search operators that add a single literal to a node s concept, a non systematic elaboration of the search space contains (among other redundancies) ....

[Article contains additional citation context not shown here]

Geoffrey I. Webb. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial IntelligenceResearch, 3:45--83, 1996.

....of any size in [1 Gamma d] is returned as the next splitting function. By contrast, DALI extends the search depth until no more monomials can be generated, and selects the beam width dynamically. DALI mainly differs from LFC on two steps: 1. A systematic search to avoid redundant combinations [22, 27], Lines 3 4, Fig. 5. Each monomial F i conjoins several boolean features (or their complements) e.g. F i = x 1 x 3 x 5 . Because conjunction is commutative, the search space is defined by avoiding any state F j that is identical to a state F i except for the order in which features appear, ....

....boolean features (or their complements) e.g. F i = x 1 x 3 x 5 . Because conjunction is commutative, the search space is defined by avoiding any state F j that is identical to a state F i except for the order in which features appear, e.g. F j = x 3 x 5 x 1 . 2. A global pruning technique [27, 17], Line 5, Fig. 5. Define F best as the best explored monomial according to some impurity measure H (e.g. entropy) such that, for all currently explored monomials F i , H(F best ) H(F i ) As long as H is monotonic, a monomial F i can be eliminated if the best value Algorithm 2: Search ....

Webb G.I.: OPUS: An Efficient Admissible Algorithm for Unordered Search. Journal of Artificial Intelligence Research, 3 (1995), 431-465

....though, its emphasis is mainly on the construction of data mining systems for end users and the modularization does not go as far as in Cheese. OPUS is a family of branch and bound search algorithms for search spaces in which the order of application of search operators is not significant. In [Web95] the authors provide detailed descriptions for efficient admissible search and dynamic search space reorderings. Pro99] describe a generic heuristic generate and test rule space search algorithm (GAT) and argue that a wide variety of knowledge discovery algorithms have as their basic underlying ....

G.I. Webb. Opus: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:431--465, 1995.

....two columns give the average number of rules generated and the average number of rules fired on each instance. RL [3] is a MetaDENDRAL style rule learner that performs a general to specific search of the space of conjunctive rules. This type of rule space search is described in detail by Webb [18]. RL uses a beam search for rules whose coverage and confidence are above user defined thresholds. In the experiments reported here, a beamsize of 100 was used along with rule constraints of confidence greater than 0.60, coverage greater than two instances, and no more than four conjuncts per ....

G. Webb. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:383--417, 1995.

....regarding the interrelation or correlation between these sets of attributes. The interestingness or usefulness of the rule is usually measured by some predefined metric function such as confidence and support [2] gain [9] chi squared value [4] gini [22] entropy gain [23, 22] laplace [6, 32], lift [16] interest [5] strength [8] and conviction [5] Several proposals for mining different types of rules according to different types of pre specified interest metrics have been suggested in the literature. The suggested techniques are fully automatic but need to have predefined tasks. ....

G. I. Webb. Opus: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, pages 431--465, 1995. 19

....volume of records defies any form of manual analysis, rendering the use of algorithms for pattern analysis indispensable. Our approach to inducing rules combines the strength of association rule mining [AMS 96] with a systematic search for rules under strong pruning techniques [Rym93, Web93, Web95, Web00] Our analysis is similar to the general framework for rule induction proposed by [Web00] but with important modifications (Section 4) We show how specific settings for the modified framework provide a principled approach to the construction of accurate rules correlating computer ....

G. I. Webb. Opus: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:431--435, 1995.

....generate the frequent itemsets, and not the association rules. MagnumOpus: MO [12] is the command line application shipped with the beta release of MagnumOpus1.2, a commercial system for association rule discovery. The main unique technique used in MagnumOpus is the search algorithm based on OPUS [11], a systematic search method with pruning. It considers the whole search space, but during the search, 3 Changing the main memory setting will not help Apriori finish the failed runs as the transactional dataset itself is not large. effectively prunes a large area of search space without missing ....

Webb, G.I. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:431-465.

....generate the frequent itemsets, and not the association rules. MagnumOpus: MO [9] is the command line application shipped with the beta release of MagnumOpus1.2, a commercial system for association rule discovery. The main unique technique used in MagnumOpus is the search algorithm based on OPUS [8], a systematic search method with pruning. It considers the whole search space, but during the search, effectively prunes a large area of search space without missing search targets provided that the targets can be measured using certain criteria. Based on this technique, MagnumOpus can ....

Webb, G.I. OPUS: An efficient admissible algorithm for unordered search. JAIR, 3:431-465.

....is to find sets of attribute value (A V) pairs with high predictive power, or contrast set mining [4, 5] where the goal is to find sets that represent large differences in the probability distributions of two or more groups. There has been much work devoted to speeding up search in set mining [6, 19] and there are many efficient algorithms when all of the data is discrete or categorical. The problem is that data is not always discrete and is typically a mix of discrete and continuous variables. A central problem for set mining and one that we address in this paper is How should continuous ....

....a size criterion and estimates how big the difference is between two distributions. We require the minimum difference in support to be greater than ffi. STUCCO finds these contrast sets using search. It uses a set enumeration tree [15] to organize the search and it uses many of the techniques in [6, 19] such as dynamic ordering of search operators, candidate groups and support bounds in conjunction with pruning rules geared for finding support differences. STUCCO also carefully controls error caused by multiple hypothesis testing (i.e. false positives) We use STUCCO as a multivariate test of ....

G. I. Webb. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:431--465, 1995.

....by the end user, and allow efficient mining of long rules should they satisfy these constraints. There are several proposals for constraint based rule mining with a machine learning instead of data mining focus that do not address the issue of efficiently dealing with large datasets. Webb [30] provides a good survey of this class of algorithms, and presents the OPUS framework which extends the set enumeration search framework of Rymon [22] with additional generic pruning methods. Webb instantiates his framework to produce an algorithm for obtaining a single rule that is optimal with ....

Webb, G. I. 1995. OPUS: An Efficient Admissible Algorithm for Unordered Search. In Journal of Artificial Intelligence Research, 3:431-465.

....a rule selection step. 4.1.1. Rule generation DC 1 uses the RL program (Clearwater and Provost 1990; Provost and Aronis 1996) to generate indicators of fraud in the form of classification rules. Similar to other MetaDENDRAL style rule learners (Buchanan and Mitchell 1978; Segal and Etzioni 1994; Webb 1995), RL performs a generalto specific search of the space of conjunctive rules. This type of rule space search is described in detail by Webb (Webb 1995) In DC 1, RL uses a beam search for rules with certainty factors above a user defined threshold. The certainty factor we used for these runs was a ....

....of fraud in the form of classification rules. Similar to other MetaDENDRAL style rule learners (Buchanan and Mitchell 1978; Segal and Etzioni 1994; Webb 1995) RL performs a generalto specific search of the space of conjunctive rules. This type of rule space search is described in detail by Webb (Webb 1995). In DC 1, RL uses a beam search for rules with certainty factors above a user defined threshold. The certainty factor we used for these runs was a simple frequency based probability estimate, corrected for small samples (Quinlan 1987) In order to deal with the very large numbers of values for ....

Webb, G. (1995). OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research 3, 383--417.

....the onset of the precursor and successor patterns is called the lag of the rule. msdd finds the k strongest dependencies in a dataset by conducting a systematic search in the space of possible dependencies. The systematicity of the search ensures that no node can ever be generated more than once [OGC95a, Rym92, Sch93, Web96]. Because non redundant expansion is achieved without access to large, rapidly changing data structures such as lists of open and closed nodes, the search space can be divided into many computationally independent subsets, each of which may be processed in parallel. Distributed msdd (dmsdd) is an ....

Geoffrey I. Webb. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:45--83, 1996.

....patterns is called the lag of the rule. msdd finds the k strongest dependencies in a dataset by conducting a systematic search in the space of possible dependencies. Systematic search expands the children of search nodes in a manner that ensures that no node can ever be generated more than once [OGC95a, RSE94, Rym92, Sch93, Web96]. Because non redundant expansion is achieved without access to large, rapidly changing data structures such as lists of open and closed nodes, the search space can be divided into many computationally independent subsets, each of which may be processed in parallel. Distributed msdd (dmsdd) is an ....

Geoffrey I. Webb. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:45--83, 1996.

....rules. Rymon [18, 19] uses systematic search with pruning to learn SE trees, a type of tree structure containing rules that predict classes using attributes. Schlimmer [20] adopts systematic search with pruning for inducing determinations that identify which factors influence others. Webb [21, 22] further explores the systematic search in a more general way. In addition, Webb [22] proposes a few new pruning rules for systematic search. 6 Conclusions and Future Work This paper has investigated a dynamic path based approach to constructing new attributes for decision tree learning. For ....

G.I. Webb, OPUS: an efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3 (1995) 431-465.

....an existing PIE, or by adding a new PIE containing a single non wildcard field. In either case, the descendants of a node are always more specific they specify more non wildcard values for fields than the original node. The search is made systematic, and therefore more efficient (Rymon 1992; Webb 1996), by only adding non wildcards and PIEs to the right of the right most non wildcard in a node when generating that node s children. Consider the node f(up )g ) f(down )g. The right most non wildcard in this rule is down in the successor. Therefore, f(up )g ) f(down router)g is a valid child, ....

....specifies all wildcards for both the precursor and the successor. The children of a node are generated by adding a single token to its precursor or successor. By imposing a total ordering on the adding of tokens, msdd ensures that each dependency rule is generated at most once (Oates et al. 1995; Webb 1996). To evaluate a rule R p R s , msdd counts co occurrences of R p and R s , and also occurrences of other precursors R p and other successors R s in the dataset. The following contingency table summarizes these counts: R s R s R p n 1 n 2 R p n 3 n 4 Msdd is interested in unusually high or low ....

Webb, G. I. 1996. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research 3:45--83.

.... events, whereas the event pattern f(down ) router)g does not: up host up host down router Systematic Search Medd s search for dependencies among events is systematic, leading to search efficiency (Oates, Gregory, Cohen 1994; Riddle, Segal, Etzioni 1994; Rymon 1992; Schlimmer 1993; Webb 1996). Systematic search non redundantly enumerates the elements of search spaces for which the value or semantics of any given node are independent of the path from the root to that node. Webb calls such search spaces unordered (Webb 1996) Consider the space of disjunctive concepts over the set of ....

....Riddle, Segal, Etzioni 1994; Rymon 1992; Schlimmer 1993; Webb 1996) Systematic search non redundantly enumerates the elements of search spaces for which the value or semantics of any given node are independent of the path from the root to that node. Webb calls such search spaces unordered (Webb 1996). Consider the space of disjunctive concepts over the set of literals fA; B; Cg. Given a root node containing the empty disjunct, false, and a set of search operators that add a single literal to a node s concept, a non systematic elaboration of the search space is shown on the left in Figure 1. ....

Webb, G. I. 1996. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research 3:45--83.

....of patterns in the streams. msdd finds the k strongest dependencies in a set of streams by performing a systematic search over the space of all possible dependencies. Systematic search expands the children of search nodes in a manner that ensures that no node can ever be generated more than once [9 12, 14]. Because non redundant expansion is achieved without access to large, rapidly changing data structures, such as lists of open and closed nodes, the search space can be divided between multiple processes on multiple machines. Only a small amount of inter process communication is required to keep ....

....of streams is systematic, leading to search efficiency and parallelizability. Systematic search nonredundantly enumerates the elements of search spaces for which the value or semantics of any given node are independent of the path from the root to that node. Webb calls such search spaces unordered [14]. Consider the space of disjunctive concepts over the set of literals fA; B; Cg. Given a root node containing the empty disjunct, false, and a set of search operators that add a single literal to a node s concept, a non systematic elaboration of the search space contains (among other redundancies) ....

[Article contains additional citation context not shown here]

Geoffrey I. Webb. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:45--83, 1996.

....1978) Several rule learners have introduced optimizations to this style of rule learning. Both RL (Clearwater and Provost 1990) and BruteDL (Segal and Etzioni 1994) use search reduction techniques, including pruning and depth bounding, to allow for massive searches of very large rule spaces. Webb (1995) introduces techniques for dynamic search space restructuring to optimize pruning, and shows that it is possible to search exhaustively for the rule that optimizes the Laplace accuracy estimate for every categorical attribute value benchmark data set in the UCI repository (Merz and Murphy 1997) ....

Webb, G. (1995). OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research 3, 383--417.

....events, whereas the event pattern f(down ) router)g does not: up host up host down router 2. 2 Systematic Search Medd s search for dependencies among events is systematic, leading to search efficiency (Oates, Gregory, Cohen 1994; Riddle, Segal, Etzioni 1994; Rymon 1992; Schlimmer 1993; Webb 1996). Systematic search non redundantly enumerates the elements of search spaces for which the value or semantics of any given node are independent of the path from the root to that node. Webb calls such search spaces unordered (Webb 1996) Consider the space of disjunctive concepts over the set of ....

....1994; Riddle, Segal, Etzioni 1994; Rymon 1992; Schlimmer 1993; Webb 1996) Systematic search non redundantly enumerates the elements of search spaces for which the value or semantics of any given node are independent of the path from the root to that node. Webb calls such search spaces unordered (Webb 1996). Consider the space of disjunctive concepts over the set of literals fA; B;Cg. Given a root node containing the empty disjunct, false, and a set of search operators that add a single literal to a node s concept, a non systematic elaboration of the search space is shown on the left in Figure 1. ....

Webb, G. I. 1996. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research 3:45--83.

....their internal search state exclusively from the persistent information in the SSM. This does not exclude local in memory representation for efficiency reasons, but this local representation must be re creatable from SSM information. To allow this even for complex search strategies such as OPUS [15], search modules can attach additional information to hypothesis objects ( spec field) In this architecture a search module inspects the current state of the search and then decides to do one of two things: ask its description generator to generate new hypotheses, or ask the quality computer ....

G.I. Webb. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3:431 -- 465, 1995.

....rules, machine learning 1 Introduction Unordered search is search in which the order in which the search operators are applied does not affect the outcome. Subset selection, a special case of unordered search where each search operator can be applied once only, has received extensive study [7, 9, 14, 19]. Pruning is critical to successful search in such spaces. Previous research has examined pruning rules that identify search operators that cannot lead to solutions and exclude those operators from consideration. These are referred to as exclusive pruning rules. This paper presents a further class ....

....In contrast, OPUS o can reorder the search space to optimize the proportion of the search space under each node. OPUS o outperforms fixed order search by optimizing the proportion of the search space pruned by each pruning action without any significant computational or storage overhead [19]. OPUS o operates by maintaining and manipulating at each node in the search tree a set of operators that may be applied below that node. These operators are called the active operators at the node. At any time during the search, there will be a set of states EXAMINED that have been ....

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Geoffrey I. Webb. OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, Volume 3, pages 431--465, 1995.

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Webb, G. I. (1995). OPUS: An efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 5, 431--465.

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G.I. Webb, OPUS: an efficient admissible algorithm for unordered search. Journal of Artificial Intelligence Research, 3, 431-465 (1995).

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