de Raedt L., Lavrac N., Dzeroski S., 1993. Multiple Predicate Learning. Procs. of the Thirteen International Joint Conference on Artificial Intelligence, Chamb'ery, France, August 28 - September 3, 1993, Vol. 2, pp. 1037-1043.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....E Theta (log 2 ( n E n E n Gamma E ) Gamma log 2 ( n I n I n Gamma I ) The total information gain is defined by: gain(P ( Y ) I gain I (P ( Y ) E gain E (P ( Y ) where I and E are such that I E = 1. A similar idea was developed in [15], although it was in a different context. These coefficients allow to control the influence of the information contained in the oe interpretations to select the literal: the more I is high, the more SPILP uses information deduced from the previous learned clauses; it is better to choose a high ....

de Raedt L., Lavrac N., Dzeroski S., 1993. Multiple Predicate Learning. Procs. of the Thirteen International Joint Conference on Artificial Intelligence, Chamb'ery, France, August 28 - September 3, 1993, Vol. 2, pp. 1037-1043.

.... logic programs, we have developed a general framework, based on a threevalued logic (ftrue, false, undefined g ) Few works, except as far as we know [1] use a three valued logic since usually, either a classical two valued logic, or a four valued logic (ftrue, false, unknown, inconsistent g ) [17, 11] is used. To handle general programs, an underlying problem is the choice of the semantics of negation. In Logic Programming, two three valued semantics are commonly used, Fitting semantics [3] and the well founded semantics [19] We present here Fitting semantics, but our framework can as well be ....

....semantics 2 . It differs from the other systems that learn general programs in I.L.P. either negation is made explicit [11] or they use the classical negation by failure [15] or completion semantics [18] or they restrict the class of general programs that can be learned (for instance in [17] they learn only stratified programs) 2 Computing the well founded semantics of general programs is more costly than computing Fitting semantics. ILP 95, Leuven This framework has been applied to the problem of single predicate learning and lead to the system ICN [8] 2 Semantics 2.1 ....

de Raedt L., Lavrac N., Dzeroski S., 1993. Multiple Predicate Learning. Proceedings of the Thirteen International Joint Conference on Artificial Intelligence, Chamb'ery, France, August 28 - September 3, 1993, Vol. 2, pp. 1037-1043.

....properties of completeness and consistency: let P q i = fe : j e 2 E q i g, for each e in E q i , bk [ q j 6=q i P q j ) C q i j= e , and for each e Gamma in E Gamma q i , bk [ q j 6=q i P q j ) C q i 6j= e Gamma . This solution leads to a global problem [16], when some definitions are mutually recursive: the union of locally complete and consistent definitions does not generally give a set of globally consistent and complete definitions. For example, the two clauses uncle(X; Y ) nephew(Y; X) and nephew(X; Y ) uncle(Y; X) can be locally consistent ....

....bias [1] is based on a well founded ordering of the elements of the domain. In this case, if the previous example is viewed in Z = 6Z, this definition that is globally satisfactory cannot yet be learned. When solving mpl problems by iterating spl techniques, an important problem pointed out in [16] is how the order the predicates are learned has an influence on the solution provided by the system. We present, in this paper, an uniform way to treat the drawbacks previously mentioned and which are due to recursive or mutually recursive definitions that lead to infinite loops. Moreover, our ....

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de Raedt L., Lavrac N., Dzeroski S., 1993. Multiple Predicate Learning. Proceedings of the Thirteen International Joint Conference on Artificial Intelligence, Chamb'ery, France, August 28 - September 3, 1993, Vol. 2, pp. 10371043.

....usually affects the correctness of other predicates that use the first one in their definitions, so revising one cannot be done without considering the others. First order theory refinement (in particular, revision) is therefore closely related to the general problem of multiple predicate learning [36], i.e. of learning theories involving multiple predicates from scratch given examples and background knowledge, so we are including multiple predicate learning systems in the survey of revision systems below even if they do not accept initial theories to start from. 2 Theory revision So let us ....

....It is important to point out, however, that this close relation is between theory revision systems and multiple predicate learning from examples systems. The multiplepredicate nature of the theories to be revised poses particular problems that do not occur when learning single predicates only [36]. Since predicates use one another in their definitions, it is insufficient, as done in many single predicate learning systems, to use only ground (atomic) background knowledge and extensionally check coverage of clauses using single clause subsumption (i.e. by mapping clause literals onto ....

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L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence. Morgan Kaufmann, 1993.

....extensional (example based) cover when determining the tness of a hypothesis. Conversely, systems that use proof based or intensional cover generally perform well on sparse data. There has also been a growing interest in multiple predicate learning within ILP. A handful of systems (Mis[19] Mpl[2], Nmpl[5] and Mult icn[10] can correctly induce programs with multiple target predicates but none can handle any amount of noise. All but Mult icn are intensional systems. In this paper we propose an ILP system, Nrmis (pronounced near miss ) which modi es Mis so it can learn from noisy ....

....correct with respect to the examples. In this situation the aim is to nd a hypothesis that has the same extension as the target hypothesis. The noise model we will use in this paper is outlined in Section 4.2. The system described in this paper addresses the ILP problem in the empirical setting [2] which requires that: the entire example set be given in advance, no queries are made of the underlying model M, and the initial hypothesis contains no de nitions for the predicates being learned. Also, we will only consider the ILP problem for de nite programs. This allows us to use ....

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L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the Thirteenth International Joint Conference on Articial Intelligence. Morgan Kaufmann, San Mateo, CA, 1993.

....extsnsions. First the candidate clauses for the different predicates are kept together in the agenda and the choice of which predicate (in fact which rule of the predicate) to learn further is left to the heuristic value of the rules. This approach is similar to the one adopted in the system MPL [RLD93] in order to tackle the problem of the order of learning different predicates (and different rules, in the case of mutually recursive predicates) Secondly, for each predicate, the other predicates in the set of multiple predicates to be learned are considered as additional abducible predicates ....

.... parent(X; Z) parent(Z; X) parent(Z; Y ) parent(Y; Z) male(X) male(Y ) male(Z) female(X) female(Y ) female(Z)g Therefore, the rules we are looking for are brother(X; Y ) sibling(X; Y ) male(X) sibling(X; Y ) parent(Z; X) parent(Z; Y ) The family database considered, taken from [RLD93] contains 16 facts about brother, 38 about sibling, 22 about parent, 9 about male and 10 about female. The background knowledge was obtained from this database by considering all the facts about male and female and only 50 of the facts about parent (selected randomly) The training set ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple Predicate Learning. In Proceedings of the 3rd International Workshop on Inductive Logic Programming, 1993.

....every negative example of E Gamma wrt the intended interpretation. However, a program which satisfies the extensional constraints is not necessarily interesting : the clause p(X) p(X) has this extensional property but does not give any information (this point has already been pointed out in [28] and [1] For system using such a method, the validation steps can prevent from creating such uninteresting clauses. 2.2 Validation of the learned program Let us first notice that, for some systems, the sole validation step is an empirical one : the system learns the expected program for some ....

....not fulfills its validation requirement. The algorithm given in figure 2 summarize this process. When several predicates are concerned, such that when learning from a database, the reduction of the complexity is important. 4. 2 Example This example of multiple predicate learning is borrowed from [28]. The knowledge base KB given in figure 3 contains informations about the sex of a group of people and their direct family relationship : male(prudent) male(willem) male(etienne) male(leon) male(rene) male(bart) male(luc) male(pieter) male(stijn) female(laura) female(esther) female(rose) ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pages 1037--1043. Morgan Kaufmann, 1993.

....both to learn new knowledge from scratch and to refine an existing background theory. 1. Introduction Studies in learning first order logic representations has followed two main trends: on one hand, many efforts have been devoted to build learning systems that are able to synthesize logic programs [5, 6, 16, 19]; on the other hand, the ability to learn and refine knowledge bases represented in first order logic languages is seen as the necessary step towards a broader class of applications. In this paper we present a prototype system, KBI (Knowledge Based Induction) that learns a knowledge base ....

....of this work was to set up the learning framework in such a way that it can be easily extended in order to face deficiencies of existing systems (e.g. working with recursive background theories, dealing with noisy data, etc. What differentiates KBI from other relational learning systems (e.g. [3, 5, 6, 12, 16, 17, 18, 19, 23]) is not a brand new search algorithm, but, rather, a more informative search structure, called LT Tree (Learned Theory Tree) that enables the system to learn a structured knowledge base limiting the complexity of the search process. The LT Tree is not a new concept: Feldman et al. 7] addressed ....

[Article contains additional citation context not shown here]

De Raedt, L., Lavrac , N., and Dz eroski, S. "Multiple Predicate Learning", Proc. of the IJCAI-93, Chambery, France, 1037-1042, 1993.

....of some of these experiments. It shows the given positive and negative example and given input output mode, followed by the definition generated. These examples involved 2 to 3 positive examples, and 1 to 8 negative examples. Input: mode( delete( delete(3, 1,2,3,4] 1,2,4] delete(5,[6,5], 6] delete(3, 1,2,5] 1,2,5] delete(7, 7,9] 7] Definition generated: delete(A,B,C) dest(B,D,E) delete(A,E,F) const(C,D,F) delete(A,B,C) dest(B,D,E) dest(E,A,F) const(C,D,F) Input: mode( extNth( extNth(s(0) 6,5,3,4] 6) extNth(s(s(0) 1,2] 2) ....

....of these experiments. It shows the given positive and negative example and given input output mode, followed by the definition generated. These examples involved 2 to 3 positive examples, and 1 to 8 negative examples. Input: mode( delete( delete(3, 1,2,3,4] 1,2,4] delete(5, 6,5] [6]) delete(3, 1,2,5] 1,2,5] delete(7, 7,9] 7] Definition generated: delete(A,B,C) dest(B,D,E) delete(A,E,F) const(C,D,F) delete(A,B,C) dest(B,D,E) dest(E,A,F) const(C,D,F) Input: mode( extNth( extNth(s(0) 6,5,3,4] 6) extNth(s(s(0) 1,2] 2) ....

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De Raedt L, Lavrac N, Dzeroski S (1993):"Multiple Predicate Learning" in Proceedings of IJCAI-93, Chamberry, France.

....objective evaluation of conditional probabilities. Keywords:discovery, data mining, error measure, conditional probability Rule Discovery: Error Measures and Conditional Rule Probabilities 1 1 Introduction Many promising rule discovery algorithms have been proposed [1] 8] 14] 27] 28] [29], 37] Most of these algorithms use their proprietary methods to discover rules. They use their own methods to . measure the error (or goodness) of rules; build the search space; and . handle or estimate the accuracy of the result. On the other hand, these algorithms share some similarities. ....

....probability difference (PD) and prediction factor (PF) are discussed and tested using DA 1. Our experiments show that using DA 1 with these evaluation functions yields correct or good rules without any application specific heuristics. Many papers suggest using heuristics in rule discovery (e.g. [29]) Rule Discovery: Error Measures and Conditional Rule Probabilities 12 However, in order to make an algorithm and the system widely applicable, as few heuristics as possible should be used. DA 1 is designed to use an error measure. That is, the smaller the value (error) the better the rule. ....

L. De Raedt, N. Lavra_, and S. Dzeroski, "Multiple Predicate Learning", Proceedings Joint International Conference on AI (IJCAI), pp. 1037-1042, 1993.

....A recently discussed notion in Inductive Logic Programming is multiple predicate learning. The idea is that instead of having just one goal predicate and training examples about one goal predicate one has several goals and training data on all these goals. Let us take the example presented in [78]. The background information consists of facts such as male(prudent) male(willem) male(etienne) male(leon) female(laura) female(esther) female(rose) female(alice) parent(bart; stijn) parent(bart; pieter) parent(luc; soetkin) parent(katleen; stijn) parent(bart; pieter) ....

....is worthwhile noting that when using decision tree classification methods [60, 61, 77] then this problem does not occur as a tree anyway classifies into mutually exclusive cases. It also does not occur in Datalog since, in contrast to Probabilistic Datalog, Datalog only produces binary decisions [78, 65]. However, Probabilistic Datalog is in general much more powerful than Datalog and can be applied to many more problems, including our profit down and profit up problem. This paper will propose methods that are used to predict categorical data (dependent goal variable) by deducing its relationship ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple Predicate Learning. In Proc Joint Int Conf on AI (IJCAI), pages 1037--1042, 1993.

....for symbolic information. However, it is not possible to take relationships between objects into account. For example, whether a firm is interesting or not can not take into account information about this firm s subcompanies. The mining for association rules [AS94] and inductive logic programming [DL93, RLD93, DSG95] are recent developments. In contrast to the other method the emphasis here is to un2 totalLandBank : F Real totalLandBank(x) sum(sizeOfLandbank(subcompanies(x) x) create derived function such that contains Figure 2: Derived function totalLandBank. cover relationships between objects and ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple Predicate Learning. In Proc Joint Int Conf on AI (IJCAI), pages 1037--1042, 1993.

....A recently discussed notion in Inductive Logic Programming is multiple predicate learning. The idea is that instead of having just one goal predicate and training examples about one goal predicate one has several goals and training data on all these goals. Let us take the example presented in [59]. The background information consists of facts such as male(prudent) male(willem) male(etienne) male(leon) female(laura) female(esther) female(rose) female(alice) parent(bart; stijn) parent(bart; pieter) parent(luc; soetkin) parent(katleen; stijn) parent(bart; pieter) ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple Predicate Learning. In Proc Joint Int Conf on AI (IJCAI), pages 1037--1042, 1993.

....in Inductive Logic Programming is multiple predicate learning. The idea is that instead of having just one goal predicate and training examples about one goal predicate one 6 LEARNING DATALOG RULES 79 has several goals and training data on all these goals. Let us take the example presented in [34]. The background information consists of facts such as male(prudent) male(willem) male(etienne) male(leon) female(laura) female(esther) female(rose) female(alice) parent(bart; stijn) parent(bart; pieter) parent(luc; soetkin) parent(katleen; stijn) parent(bart; pieter) ....

....than FOIL or GOLEM for multiple predicate learning. Question 29 Verify the last claim by taking a concrete example (for instance the family relationship example suggested previously) of some background facts and noise free positive and negative training examples. Furthermore, since also the study [34] does not allow noise to occur simply take the algorithm of section 6.1 and any choice strategy. We next discuss techniques to learn probabilistic concepts and make also a comparison to neural net learning approaches. 7 LEARNING PROBABILISTIC KNOWLEDGE 80 7 Learning Probabilistic Knowledge The ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple Predicate Learning. In Proc Joint Int Conf on AI (IJCAI), pages 1037--1042, 1993.

....rule solutions effectively, DA 2 is requested to discover the relationships husband, parent, and grand parent from the background information involving predicates male, female, father, and mother. Ideally, the system is expected to discover the set of rules shown in Figure 3 ([19] shows how to learn all these rule sets at once) Fig 3 : ideal rule sets To ensure a fair evaluation of the performance of DA 2, the following two sets of test data are prepared: 1) Complete set of background information, complete set of positive examples and about 250 randomly selected ....

L. De Raedt, N. Lavrac, and S. Dzeroski, Multiple Predicate Learning, Proceedings Joint International Conference on AI (IJCAI), pp. 1037-1042, 1993.

....approximation of the theory. Although theory revision systems have been around ever since MARVIN [124] MIS [125] followed by Banerji [4] BLIP MOBAL [147] ML SMART [9] CIGOL [89] and CLINT [108] there has recently been a renewed interest in theory revision and multiple predicate learning, cf. [2, 1, 6, 115, 118, 146, 28, 10, 134, 113, 148, 110]. These newer approaches differ from the previous ones in the sense that they try to learn without requiring an oracle. Note that also ML SMART and BLIP MOBAL did not require an oracle. Although it is commonly believed that theory revision and multiple predicate learning algorithms are ....

....is based on a simple general to specific iterative deepening search using refinement under subsumption. At the same time, it offers a natural approach to empirically learning multiple predicates, which requires interaction with the user, or good presentations in the normal setting (see [114, 115]) Indeed, in the nonmonotonic setting it is easy to learn multiple predicates, because if two clauses c 1 and c 2 are valid, then their conjunction is also valid. This is in contrast to the normal setting, where the conjunction of two clauses (contributing individually to a solution) may violate ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence. Morgan Kaufmann, 1993.

....errors (called noise) see [23] In Table 1 we sketch some well known ILP systems along these five dimensions. The ILP systems sketched are: systems that induce predicate definitions in the normal ILP setting MIS [42] CLINT [8] MOBAL [20] CIGOL [32] FOIL [40] GOLEM [34] LINUS [24, 23] MPL [14] and, on the other hand, CLAUDIEN [12] which 3. ILP TECHNIQUES 235 System Emp Inc Int No Inv No Sin Mul Noise No MIS Inc Int No Mul No CLINT Inc Int Inv Mul No MOBAL Inc No Inv Mul No CIGOL Inc Int Inv Mul No FOIL Emp No No Sin Noise GOLEM Emp No No Sin Noise LINUS Emp No No Sin Noise MPL Emp No ....

....(logical) definitions [36, 4] of these notions: Definition 3.1 (Semantic generalization) A hypothesis H 1 is semantically more general than a hypothesis H 2 with respect to theory B if and only if B [ H 1 j= H 2 . 4 FOIL and GOLEM should not be regarded as multiple predicate learners, cf. [14] and Section 5. 236 Multiple Predicate Learning in Two Inductive Logic Programming Settings Definition 3.2 (Syntactic generalization or subsumption) A clause c 1 (a set of literals) is syntactically more general than a clause c 2 if and only if there exists a substitution such that c 1 ....

[Article contains additional citation context not shown here]

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pages 1037--1042. Morgan Kaufmann, 1993.

....in arguments mfoil icl 55 60 65 70 75 80 85 90 95 100 0 5 10 15 20 30 50 80 noise in argument and class mfoil icl Fig. 7. Results of the King Rook King experiment all clauses are considered independent constraints, whereas in ILP clauses may be mutually dependent, complicating coverage tests [ De Raedt et al. 1993 ] Fourth, the clausal logic we employ allows to easily express some concepts which are hard (or impossible) to express using the normal inductive logic programming paradigm and definite clauses. For instance, a concept such as all wagons are black or white, can very naturally be represented by ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pages 1037--1042. Morgan Kaufmann, 1993.

....already indicate that learning from satisfiability is more complicated than learning from interpretations. In this respect, learning from satisfiability is closer to learning from entailment, where monotonicity does not hold either (when learning multiple or recursive predicate definitions, cf. [De Raedt et al. 1993]) This is no surprise as learning from satisfiability can be considered a generalization of learning from entailment. 5 Algorithms In this section two algorithms are proposed for learning from satisfiability. The first algorithm performs characteristic induction and is integrated in the clausal ....

....grammar for parsing ultra simple sentences in English. More specifically, the aim was to induce the following DCG: sent(A; B) np(A; C) vp(C; B) np(A; B) det(A; C) noun(C; B) vp(A; B) verb(A; B) vp(A; B) verb(A; C) np(C; B) Notice that this is a multiple predicate learning problem (cf. [De Raedt et al. 1993]) For the purposes of this experiment Claudien Sat, i.e. the characteristic inducer, was employed. Claudien Sat s DLAB mechanism was used to assure that 1) only clauses in DCG form would be derived. 2) each clause in hypothesis should define a non terminal (i.e. sent, np or vp) and 3) at most 3 ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pages 1037--1042. Morgan Kaufmann, 1993.

.... clauses; for instance, the following theory could be constructed at once from appropriate evidence: daughter(Y,X) parent(X,Y) female(Y) female(X) daughter(X,Y) parent(Y,X) daughter(X,Y) This method of delayed signing of literals is related to the multiple predicate learning approach of (De Raedt et al. 1993): their MPL algorithm constructs clause bodies separately, dynamically deciding with which clause head to combine. Finally, we mention that (De Raedt, 1996) also discusses the duality between DNF and CNF as representations for hypotheses. A CNF learning problem can be transformed to a DNF learning ....

L. De Raedt, N. Lavrac & S. Dzeroski. Multiple predicate learning. Proc. 13th Int. Joint Conf. on Artificial Intelligence, pp.1037--1042. Morgan Kaufmann, 1993.

....level. 2.3 Constraints on PILP The conclusion for the normal setting, should be that partitioning is only permitted if one is learning a single predicate without recursion. This finding is in line with previously reported results on the comparable problem of Multiple Predicate Learning (cf. [3]) For the nonmonotonic setting, valid partions of an ILP task can be produced by splitting up the language bias L. 2 Sometimes, see [1, 7] one also requires minimality, which means that the hypothesis should not contain redundant clauses. 3 Experimental evaluation 3.1 Experimental setup ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pages 1037--1042. Morgan Kaufmann, 1993.

....setting of inductive logic programming. Two important consequences of this are that the PAC learning results for our setting are much better than those for the normal setting (see [6, 11, 16] and that there are problems in the normal setting when learning multiple predicates (see for instance [8]) One of the main contributions of this paper will be to show that a variety of different discovery tasks fit in this logical paradigm. In particular, we will show how apparently different discovery tasks can be obtained by varying the set of well formed clauses in L. As our aim is to design a ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence. Morgan Kaufmann, 1993.

....and H 2 is consistent with respect to a background theory B and a set of observations O, then H 1 [ H 2 need not be consistent with O. This property is the cause of some well known problems when learning multiple predicates or recursive predicates in the explanatory induction setting, cf. [De Raedt et al. 1993; Bergadano and Gunetti, 1993; Cameron Jones and Quinlan, 1993] The reason for this is that inconsistencies may arise when H 1 and H 2 can resolve together. Flach s [Flach, 1992] definition of weak induction (from which his later notion of confirmatory induction is derived) is the special case of ....

L. De Raedt, N. Lavrac, and S. Dzeroski. Multiple predicate learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pages 1037--1042. Morgan Kaufmann, 1993.

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De Raedt, L., Lavrac , N., and Dz eroski, S. "Multiple Predicate Learning", Proc. of the IJCAI-93, Chambery, France, 1037-1042, 1993.

No context found.

De Raedt, L., Lavrac, N., Dzeroski, S. (1993): "Multiple Predicate Learning" in Proceedings of IJCAI-93, Chamberry, France.

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