## OPUS: An Efficient Admissible Algorithm for Unordered Search (1995)

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Citations: | 82 - 14 self |

### BibTeX

@MISC{Webb95opus:an,

author = {Geoffrey I. Webb},

title = {OPUS: An Efficient Admissible Algorithm for Unordered Search},

year = {1995}

}

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### Abstract

OPUS is a branch and bound search algorithm that enables efficient admissible search through spaces for which the order of search operator application is not significant. The algorithm's search efficiency is demonstrated with respect to very large machine learning search spaces. The use of admissible search is of potential value to the machine learning community as it means that the exact learning biases to be employed for complex learning tasks can be precisely specified and manipulated. OPUS also has potential for application in other areas of artificial intelligence, notably, truth maintenance.

### Citations

1077 |
A formal basis for the heuristic determination of minimum cost paths
- Hart, Nilsson, et al.
- 1968
(Show Context)
Citation Context ... be expanded in a best-first manner, with the benefits outlined above. 5.2.2 Relation to Previous Search Algorithms OPUS o can be viewed as an amalgamation of FSS (Narendra & Fukunaga, 1977) with A* (=-=Hart, Nilsson, & Raphael, 1968-=-). FSS performs branch and bound search in unordered search spaces, traversing the search space so as to visit each state at most once and dynamically organizing the search tree so as to maximize the ... |

947 | A theory of diagnosis from first principles - Reiter - 1987 |

807 | The CN2 induction algorithm
- Clark, Niblett
- 1989
(Show Context)
Citation Context ...ions that maximize the Laplace accuracy estimate with respect to a training set of preclassified example objects. This is, for example, the search task that CN2 purports to heuristically approximate (=-=Clark & Niblett, 1989-=-) when forming the disjuncts of a disjunc450sAn Efficient Admissible Algorithm for Unordered Search tive classifier. Machine learning systems have employed OPUS o in this manner to develop rules for i... |

787 |
UCI repository of machine learning databases
- Murphy, Aha
- 1994
(Show Context)
Citation Context ... function was employed to prune nodes at Step 8 of the OPUS o algorithm. 6.2 Experimental Method This search was performed on fourteen data sets from the UCI repository of machine learning databases (=-=Murphy & Aha, 1993-=-). These were all the data sets from the repository that the researcher could at the time of the experiments identify as capable of being readily expressed as a categorical attribute-value learning ta... |

728 |
Heuristics: Intelligent Search Strategies for Computer Problem Solving
- Pearl
- 1984
(Show Context)
Citation Context ...o be used with non-admissible pruning heuristics to obtain efficient non-admissible search. The OPUS algorithms are not only admissible (when used with admissible pruning rules), they are systematic (=-=Pearl, 1984-=-). That is, in addition to guaranteeing that a goal will be found if one exists, the algorithms guarantee that no state will be visited more than once during a search (so long as it is not possible to... |

705 |
A Theory and Methodology of Inductive Learning
- Michalski
- 1983
(Show Context)
Citation Context ...of equality expressions cannot express a �= x, whereas a language restricted to conjunctions of inequality expressions can express a = x using the expression a �= y ∧ a �= z. In internal disjunctive (=-=Michalski, 1984-=-) terms, a �= x is equivalent to a = y or z. It should be noted that— • For attributes with more than two values the search space for conjunctions of inequality expressions is far larger than the sear... |

469 | An assumption-based TMS - Kleer - 1986 |

341 | Rule induction with CN2: Some recent improvements
- Clark, Boswell
- 1991
(Show Context)
Citation Context ... the most general expression, true. Each operator performs conjunction of the current expression with a term A �= v, where A is an attribute and v is any single value for that attribute. The Laplace (=-=Clark & Boswell, 1991-=-) preference function was used to determine the goal of the search. This function provides a conservative estimate of the predictive accuracy of a class description, e. It is defined as value(e)= posC... |

201 |
A branch and bound algorithm for feature subset selection
- &Fukunaga, K
- 1977
(Show Context)
Citation Context ...ype of search problem, search through unordered search spaces, that is the subject of this investigation. Special cases of search through unordered search spaces are provided by the subset selection (=-=Narendra & Fukunaga, 1977-=-) and minimum test-set (Moret & Shapiro, 1985) search problems. Subset selection involves the selection of a subset of objects that maximizes an evaluation criterion. The minimum test-set problem invo... |

195 | The need for biases in learning generalizations
- Mitchell
- 1980
(Show Context)
Citation Context ... will usually require a strong inductive bias in the class description language (restriction on the types of class descriptions that will be considered) if they are to find useful class descriptions (=-=Mitchell, 1980-=-). SE-tree-based learning (Rymon, 1993) demonstrates admissible search for a set of consistent class descriptions within more complex class description languages than may usefully be employed with the... |

156 |
Problem Solving Methods in Artificial Intelligence
- Nilsson
- 1971
(Show Context)
Citation Context ..., heuristic algorithms cannot guarantee that they will find the targets they seek. In contrast, an admissible search algorithm is one that is guaranteed to uncover the nominated target, if it exists (=-=Nilsson, 1971-=-). This greater utility is usually obtained at a significant computational cost. This paper describes the OPUS (Optimized Pruning for Unordered Search) family of search algorithms. These algorithms pr... |

133 |
Version spaces: A candidate elimination approach to rule learning
- Mitchell
- 1977
(Show Context)
Citation Context ...ng classifiers that are consistent with a training set of examples. The two classic algorithms for this purpose are the least generalization algorithm (Plotkin, 1970) and the version space algorithm (=-=Mitchell, 1977-=-). The least generalization algorithm finds the most specialized class description that covers all objects in a training set containing only positive examples. The version space algorithm finds all cl... |

116 |
Search Through Systematic Set Enumeration
- Rymon
- 1992
(Show Context)
Citation Context ...ng a sole goal node from that search tree. The OPUS algorithms differ from most previous admissible search algorithms employed in machine learning (Clearwater & Provost, 1990; Murphy & Pazzani, 1994; =-=Rymon, 1992-=-; Segal & Etzioni, 1994; Webb, 1990) in that when such operators are identified, they are removed from consideration in all branches of the search tree that descend from the current node. In contrast,... |

95 | An information theoretic approach to rule induction from databases - Smyth, Goodman - 1992 |

88 | Oversearching and layered search in empirical learning - Quinlan - 1995 |

74 |
A Note on Inductive Generalisation
- Plotkin
- 1970
(Show Context)
Citation Context ... admissible search algorithms exist for developing classifiers that are consistent with a training set of examples. The two classic algorithms for this purpose are the least generalization algorithm (=-=Plotkin, 1970-=-) and the version space algorithm (Mitchell, 1977). The least generalization algorithm finds the most specialized class description that covers all objects in a training set containing only positive e... |

68 | Efficiently inducing determinations: a complete and systematic search algorithm that uses optimal pruning
- Schlimmer
- 1993
(Show Context)
Citation Context ...application of different sets of operators). 3. Fixed-order Search A number of recent machine learning algorithms have performed restricted admissible search (Clearwater & Provost, 1990; Rymon, 1993; =-=Schlimmer, 1993-=-; Segal & Etzioni, 1994; Webb, 1990). All of these algorithms are based on an organization of the search tree, that, when considering the search problem illustrated in Figures 1 to 3, traverse the sea... |

63 |
Branch and Bound Methods - A Survey
- Lawler, Wood
- 1966
(Show Context)
Citation Context ...lly to both variants the name OPUS will be employed. When a comment applies to only one variant of the algorithm, it will be distinguished by its respective superscript. OPUS uses a branch and bound (=-=Lawler & Wood, 1966-=-) search strategy that traverses the search space in a manner similar to that illustrated in Figure 4 so as to guarantee that no two equivalent nodes in the search space are both visited. However, it ... |

61 | Exploring the decision forest: an empirical investigation of Occam’s razor in decision tree induction
- Murphy, Pazzani
- 1994
(Show Context)
Citation Context ...g from n without excluding a sole goal node from that search tree. The OPUS algorithms differ from most previous admissible search algorithms employed in machine learning (Clearwater & Provost, 1990; =-=Murphy & Pazzani, 1994-=-; Rymon, 1992; Segal & Etzioni, 1994; Webb, 1990) in that when such operators are identified, they are removed from consideration in all branches of the search tree that descend from the current node.... |

52 |
RL4: A tool for knowledge-based induction
- Clearwater, Provost
- 1990
(Show Context)
Citation Context ...in the search tree descending from n without excluding a sole goal node from that search tree. The OPUS algorithms differ from most previous admissible search algorithms employed in machine learning (=-=Clearwater & Provost, 1990-=-; Murphy & Pazzani, 1994; Rymon, 1992; Segal & Etzioni, 1994; Webb, 1990) in that when such operators are identified, they are removed from consideration in all branches of the search tree that descen... |

43 | Generalizing version spaces - Hirsh - 1994 |

39 | Characterizing Diagnoses - Kleer, Mackworth, et al. |

34 | An SE-tree based characterization of the induction problem
- Rymon
- 1993
(Show Context)
Citation Context ...ngle node by application of different sets of operators). 3. Fixed-order Search A number of recent machine learning algorithms have performed restricted admissible search (Clearwater & Provost, 1990; =-=Rymon, 1993-=-; Schlimmer, 1993; Segal & Etzioni, 1994; Webb, 1990). All of these algorithms are based on an organization of the search tree, that, when considering the search problem illustrated in Figures 1 to 3,... |

27 |
On minimizing a set of tests
- Moret, Shapiro
- 1985
(Show Context)
Citation Context ...earch spaces, that is the subject of this investigation. Special cases of search through unordered search spaces are provided by the subset selection (Narendra & Fukunaga, 1977) and minimum test-set (=-=Moret & Shapiro, 1985-=-) search problems. Subset selection involves the selection of a subset of objects that maximizes an evaluation criterion. The minimum test-set problem involves the selection of a set of tests that max... |

20 | Systematic search for categorical attribute-value data-driven machine learning
- Webb
- 1993
(Show Context)
Citation Context ...450sAn Efficient Admissible Algorithm for Unordered Search tive classifier. Machine learning systems have employed OPUS o in this manner to develop rules for inclusion both in sets of decision rules (=-=Webb, 1993-=-) and in decision lists (Webb, 1994b). (The current experiments were performed using the Cover learning system, which, by default, performs repeated search for pure conjunctive classifiers within a CN... |

10 | Implementing Valiant’s Learnability Theory using Random Sets - Oblow - 1990 |

9 | A heuristic programming study of theory formation in science
- Buchanan, Feigenbaum, et al.
- 1971
(Show Context)
Citation Context ...Figure 2: Simple unordered operator search tree with pruning beyond application of operator c called fixed-order search. (Fixed-order search has also been used for non-admissible search, for example, =-=Buchanan, Feigenbaum, & Lederberg, 1971-=-). Figure 5 illustrates the effect of pruning the sub-tree descending below operator c, under fixed-order search. As can be seen, this is substantially less effective than the optimized pruning illust... |

7 | Generality is more significant than complexity: Toward an alternative to occam’s razor
- Webb
- 1994
(Show Context)
Citation Context ...a highly specific classification rule. The goal of this search is to uncover the set of all most general rules that cover identical objects in the training data to those covered by the original rule (=-=Webb, 1994-=-a). 5.2 OPUSo A number of changes are warranted if OPUS is to be applied to optimization search. The following definition of OPUSo , a variant of OPUS for optimization search, assumes that two domain ... |

6 | Techniques for efficient empirical induction
- Webb
- 1990
(Show Context)
Citation Context ... tree. The OPUS algorithms differ from most previous admissible search algorithms employed in machine learning (Clearwater & Provost, 1990; Murphy & Pazzani, 1994; Rymon, 1992; Segal & Etzioni, 1994; =-=Webb, 1990-=-) in that when such operators are identified, they are removed from consideration in all branches of the search tree that descend from the current node. In contrast, the other algorithms only remove a... |

2 |
464 Efficient Admissible Algorithm for Unordered Search
- Segal, Etzioni
- 1994
(Show Context)
Citation Context ...l node from that search tree. The OPUS algorithms differ from most previous admissible search algorithms employed in machine learning (Clearwater & Provost, 1990; Murphy & Pazzani, 1994; Rymon, 1992; =-=Segal & Etzioni, 1994-=-; Webb, 1990) in that when such operators are identified, they are removed from consideration in all branches of the search tree that descend from the current node. In contrast, the other algorithms o... |

2 | Techniques for e#cient empirical induction - Webb - 1990 |