L. Watanabe and L. Rendell. Learning structural decision trees from examples. In Proceedings of the Eighth International Workshop on Machine Learning, Ithaca, New York, 1991. Morgan Kaufmann.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[ Quinlan, 1990b ] the concept description language of Horn clause logic is perhaps unnecessarily restrictive; it may be possible to extend the power of the language somewhat without giving up the two advantages of efficiency and perspicuity. The learning techniques described in [ Cohen, 1991a; Watanabe and Rendell, 1991 ] for extensions of decision trees may be useful in this regard. Of course, FOIL s run time is exponential in the arity of the feature predicates, so the asymptotic complexity of the two algorithms is the same. However, it is often more practical to use an algorithm which has long run time than ....

L. Watanabe and L. Rendell. Learning structural decision trees from examples. In Proceedings of the Eighth International Workshop on Machine Learning, Ithaca, New York, 1991. Morgan Kaufmann.

.... improvements (Cussens, 1997) Other directions are the use of sampling techniques and stochastic methods, such as proposed by, e.g. Srinivasan (1999) and Sebag (1998) Finally, the Tilde system is related to other systems that induce first order decision trees, such as the Struct system (Watanabe and Rendell, 1991) (which uses a less explicitly logic based approach) and the regression tree learner SRT (Kramer, 1996) 36 7. Conclusions We have argued and demonstrated empirically that the use of ILP is not limited to small databases, as is often assumed. Mining databases of a hundred megabytes was shown to ....

L. Watanabe and L. Rendell. Learning structural decision trees from examples. In Proceedings of the 12th International Joint Conference on Artificial Intelligence, pages 770--776, 1991.

....existence of associations, we also use the multiplicity of available associations in order to further prune the search space. This is explained in more detail in [8, 9] Multi relational decision trees The induction of decision trees in first order logic has been studied by several researchers [2, 3, 10, 18]. Each of these approaches share a common Divide and Conquer strategy, but produce different flavours of decision trees. For example [10] discusses the induction of regression trees, whereas [3] discusses the induction of decision trees for clustering. In [2] an overview is given of potential uses ....

Watanabe, L., Rendell, L. Learning structural decision trees from examples, In Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI'91), 770-776, 1991

....specialising an overly general clause, on each iteration selecting a specialised clause that covers a subset of the positive examples and no negative examples, until all positive examples are covered by the selected clauses. Divide and Conquer, which has been used in e.g. ml smart [1] struct [27], idel [13] and spectre [7] constructs a hypothesis by dividing an overly general clause into a set of clauses, which correspond to disjoint subsets of the examples. It then continues recursively with those clauses for which the corresponding subsets contain both positive and negative examples. ....

....it should be noted that the non deterministic choices (in this case of which literals to unfold upon) are crucial for the result when applying Divide and Conquer. Again, the optimal choices can be approximated by selecting the specialisation that maximises the information gain, as is done in [27, 12, 7] (cf. id3 [23] This is equivalent to minimising: Gammac n X i=1 cov(C i ; E ) log 2 cov(C i ; E ) cov(C i ; E [ E Gamma ) cov(C i ; E Gamma ) log 2 cov(C i ; E Gamma ) cov(C i ; E [ E Gamma ) where C 1 ; Cn are the resolvents upon one of the ....

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Watanabe L. and Rendell L., "Learning Structural Decision Trees from Examples", Proceedings of the Twelvth International Joint Conference on Artificial Intelligence, Morgan Kaufmann (1991) 770--776 29

.... Lookahead for construction of Boolean feature combinations is also considered in [515] Linear threshold unit trees for Boolean functions are described in [418] Decision trees having first order predicate calculus representations, with Horn clauses as tests at internal nodes, are considered in [497]. Subsample selection Feature subset selection attempts to choose useful features. Similarly, subsample selection attempts to choose appropriate training samples for induction. Quinlan suggested windowing , a random training set sampling method, for his programs ID3 and C4.5 [398, 506] A ....

Larry Watanabe and Larry Rendell. Learning structural decision trees from examples. In IJCAI-91 [220], pages 770--776. Editors: John Mylopoulos and Ray Reiter.

....induction of decision trees mostly for two important reasons: ffl Unknown values can be dealt with pragmatically: never incorporate tests for unknown in a rule. ffl Induction focuses on one class at a time. At least in relational learning this approach seems to be superior to decision trees [Watanabe Rendell 91] and we suspect that the same might be true for propositional learning. 1 One might argue whether dropping an attribute really is a constructive induction operator or not. Anyway it being a very useful operator we have chosen to include it in the above list. Furthermore the terminology used in ....

Watanabe L., Rendell L.: Learning Structural Decision Trees from Examples, in Proceedings of the 12th International Conference on Artificial Intelligence, Morgan Kaufmann, San Mateo, CA, pp.770-776, 1991.

.... topdown induction of logic programs (mis [Shapiro 1983] foil [Quinlan 1990] ana ebl [Cohen 1991] focl [Pazzani et al. 1991] grendel [Cohen 1992] and focl frontier [Pazzani and Brunk 1993] while the latter has been used in a few approaches (ml smart [Bergadano and Giordana 1988] struct [Watanabe and Rendell 1991] and spectre [Bostrom and Idestam Almquist 1994] The major advantage of divide and conquer over covering is the efficiency, as demonstrated in [Bostrom 1995] The reason for this is that covering in fact searches a larger hypothesis space than what divide and conquer does and that covering ....

Watanabe L. and Rendell L. "Learning Structural Decision Trees from Examples", Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, Morgan Kaufmann, CA, 1991, 770--776.

.... Lookahead for construction of Boolean feature combinations is also considered in [389] Linear threshold unit trees for Boolean functions are described in [321] Decision trees having first order predicate calculus representations, with Horn clauses as tests at internal nodes, are considered in [375]. 5.1.3. Subsample selection Feature subset selection attempts to choose useful features. Similarly, subsample selection attempts to choose appropriate training samples for induction. Quinlan suggested windowing , a random training set sampling method, for his programs ID3 and C4.5 [306, 382] A ....

Larry Watanabe and Larry Rendell. Learning structural decision trees from examples. volume 2, pages 770--776, Darling Harbour, Sydney, Australia, 24--30th, August 1991. Morgan Kaufmann Pub. Inc., San Mateo, CA. Editors: John Mylopoulos and Ray Reiter.

....a frame based language that is equivalent to first order predicate calculus. KATE makes extensive use of a given hierarchy and heuristics to generate the branch tests. To our knowledge, KATE was the first system to induce first order theories in a divide and conquer fashion. Watanabe and Rendell [29] also investigated the use of divide and conquer for learning first order theories. Although their so called structural decision trees are used for the prediction of categorical classes and not continuous classes, it is the closest work found in the literature. 3 Description of the Method 3.1 ....

L. Watanabe and L. Rendell, `Learning structural decision trees from examples ', in Proc. Twelfth International Joint Conference on Artificial Intelligence (IJCAI-91), pp. 770--776, San Mateo, CA, (1991). Morgan Kaufmann.

....trees for various reasons. The two most important ones are: ffl Unknown values can be dealt with pragmatically: never incorporate tests for unknown in a rule. ffl Induction focuses on one class at a time. At least in relational learning this approach seems to be superior to decision trees [Watanabe Rendell 91] and we suspect that the same might be true for propositional learning. Currently the learner is a quick and dirty custom implementation, as we want to focus on constructive induction, but still like to have the possibility of working on the internals of the learner. We will of course have to ....

Watanabe L., Rendell L.: Learning Structural Decision Trees from Examples, in Proceedings of the 12th International Conference on Artificial Intelligence, Morgan Kaufmann, San Mateo, CA, pp.770-776, 1991.

....on covering strategies (cf. Bostrom, 1995 ] Within attribute value learning (or propositional concept learning) TDIDT is more popular than the covering approach. Yet, within first order approaches to concept learning, only a few learning systems have made use of decision tree techniques ( Watanabe and Rendell, 1991; Bergadano and Giordana, 1988 ] and in the field of inductive logic programming, the approach has almost totally been ignored. With the exception of [ Bostrom, 1995 ] and some systems that transform ILP problems into propositional form (e.g. LINUS [ Lavrac and Dzeroski, 1994 ] Indigo [ ....

....a decision tree. Our main contribution is the introduction of a logical decision tree representation that corresponds to a clausal representation. Logical decision trees upgrade the attribute value representations used within classical TDIDT algorithms, and also generalize the earlier work by [ Watanabe and Rendell, 1991 ] Given the logical decision tree representation, it is easy to design and implement an algorithm for top down induction of logical decision trees by adapting C4.5 s heuristics. This results in the Tilde system, which is the main topic of this paper. Tilde works within the learning from ....

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L. Watanabe and L. Rendell. Learning structural decision trees from examples. In Proceedings of the 12th International Joint Conference on Artificial Intelligence, pages 770--776, 1991.

....whereas the INFO function determines whether C, p(C) p 0 (C) or possibly something else is stored. Most (classification or regression) tree induction systems that exist today are instantiations of this generic algorithm: we mention C4.5 (Quinlan, 1993a) Cart (Breiman et al. 1984) Struct (Watanabe and Rendell, 1991), SRT (Kramer, 1996) The main exceptions are incremental decision tree learners (Utgoff, 1989; Chapman and Kaelbling, 1991) These systems typically build the tree top down, but contain operators for changing the tree when new evidence suggests to do so (by changing tests, rearranging ....

....programming that has dominated the research on relational learning techniques during the latest decennium (in the form of inductive logic programming) relational hypotheses are almost always represented as first order rule sets. A few exceptions exist; we mention Kate (Manago, 1989) Struct (Watanabe and Rendell, 1991), ML Smart (Bergadano and Giordana, 1988) SRT (Kramer, 1996) and Tritop (Geibel and Wysotzki, 1997) Not all of these systems operate within a strict logical framework; e.g. Kate uses a frame based representation language. There is also some variation in certain restrictions that are imposed. ....

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L. Watanabe and L. Rendell. Learning structural decision trees from examples. In Proceedings of the 12th International Joint Conference on Artificial Intelligence, pages 770--776, 1991.

....if Q succeeds, exactly one of Q; T:test (which is equivalent to Q; p i ) and Q; not(p i ) must succeed. This is not the case, however, with Q; T:test and Q; not(T:test) when T:test shares variables with Q. This complication was ignored in earlier work on relational decision trees [WR91, Kra96] For an illustration of this, consider in Figure 4 the node containing not replaceable(X) The query associated to the right subtree of this node contains the negation of the predicate p 1 associated with that node, and not just the negation of the added literal. Indeed, there is a ....

....to the learning from interpretations setting) Experiments show that logical decision trees have good potential for efficiently finding simple theories that have high predictive accuracy, for a broad range of problems. Of the existing decision tree approaches within relational learning, Struct[WR91] and SRT[Kra96] are closest to ours. However, all this work has focused on induction techniques and has largely ignored the logical and representational aspects of decision trees, needed to fully understand the potential of this technique for first order learning. Bostrom [Bos95] has compared ....

L. Watanabe and L. Rendell. Learning structural decision trees from examples. In Proceedings of the 12th International Joint Conference on Artificial Intelligence, pages 770--776, 1991.

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Larry Watanabe and Larry Rendell. Learning structural decision trees from examples. volume 2, pages 770#776, Darling Harbour, Sydney, Australia, 24#30th, August 1991. Morgan Kaufmann Pub. Inc., San Mateo, CA. Editors: John Mylopoulos and Ray Reiter.

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