Results 1  10
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23
Incremental concept learning for bounded data mining
 Information and Computation
, 1999
"... Important re nements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every in nite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning ma ..."
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Cited by 39 (29 self)
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Important re nements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every in nite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning machine computes a sequence of hypotheses about the target concept from a positive presentation of it. With iterative learning, the learning machine, in making a conjecture, has access to its previous conjecture and the latest data item coming in. In kbounded examplememory inference (k is a priori xed) the learner is allowed to access, in making a conjecture, its previous hypothesis, its memory of up to k data items it has already seen, and the next element coming in. In the case of kfeedback identi cation, the learning machine, in making a conjecture, has access to its previous conjecture, the latest data item coming in, and, on the basis of this information, it can compute k items and query the database of previous data to nd out, for each of the k items, whether or not it is in the database (k is again a priori xed). In all cases, the sequence of conjectures has to converge to a hypothesis
Finding Minimal Generalizations for Unions of Pattern Languages and Its Application to Inductive Inference from Positive Data.
 In Proc. the 11th STACS, LNCS 775
, 1994
"... A pattern is a string of constant symbols and variables. The language defined by a pattern p is the set of constant strings obtained from p by substituting nonempty constant strings for variables in p. In this paper we are concerning with polynomial time inference from positive data of the class of ..."
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Cited by 23 (12 self)
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A pattern is a string of constant symbols and variables. The language defined by a pattern p is the set of constant strings obtained from p by substituting nonempty constant strings for variables in p. In this paper we are concerning with polynomial time inference from positive data of the class of unions of a bounded number of pattern languages. We introduce a syntactic notion of minimal multiple generalizations (mmg for short) to study the inferability of classes of unions. If a pattern p is obtained from another pattern q by substituting nonempty patterns for variables in q, q is said to be more general than p. A set of patterns defines a union of their languages. A set Q of patterns is said to be more general than a set P of patterns if for any pattern p in P there exists a more general pattern q in Q than p. Clearly more general set of patterns defines larger unions. A kminimal multiple generalization (kmmg) of a set S of strings is a minimally general set of at most k pattern...
Angluin's Theorem for Indexed Families of R.e. Sets and Applications
, 1996
"... We extend Angluin's (1980) theorem to characterize identifiability of indexed families of r.e. languages, as opposed to indexed families of recursive languages. We also prove some variants characterizing conservativity and two other similar restrictions, paralleling Zeugmann, Lange, and Kapur's (199 ..."
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Cited by 14 (0 self)
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We extend Angluin's (1980) theorem to characterize identifiability of indexed families of r.e. languages, as opposed to indexed families of recursive languages. We also prove some variants characterizing conservativity and two other similar restrictions, paralleling Zeugmann, Lange, and Kapur's (1992, 1995) results for indexed families of recursive languages. 1 Introduction A significant portion of the work of recent years in the field of inductive inference of formal languages, as initiated by Gold 1967, stems from Angluin's (1980b) theorem, which characterizes when an indexed family of recursive languages is identifiable in the limit from positive data in the sense of Gold. Up until around 1980, a prevalent view had been that inductive inference from positive data is too weak to be of much theoretical interest. This misconception was due to the negative result in Gold's original paper, which says that any class of languages that contains every finite language and at least one infini...
Elementary formal systems, intrinsic complexity, and procrastination
 Information and Computation
, 1997
"... Recently, rich subclasses of elementary formal systems (EFS) have been shown to be identifiable in the limit from only positive data. Examples of these classes are Angluin’s pattern languages, unions of pattern languages by Wright and Shinohara, and classes of languages definable by lengthbounded e ..."
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Cited by 13 (6 self)
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Recently, rich subclasses of elementary formal systems (EFS) have been shown to be identifiable in the limit from only positive data. Examples of these classes are Angluin’s pattern languages, unions of pattern languages by Wright and Shinohara, and classes of languages definable by lengthbounded elementary formal systems studied by Shinohara. The present paper employs two distinct bodies of abstract studies in the inductive inference literature to analyze the learnability of these concrete classes. The first approach, introduced by Freivalds and Smith, uses constructive ordinals to bound the number of mind changes. ω denotes the first limit ordinal. An ordinal mind change bound of ω means that identification can be carried out by a learner that after examining some element(s) of the language announces an upper bound on the number of mind changes it will make before converging; a bound of ω · 2 means that the learner reserves the right to revise this upper bound once; a bound of ω · 3 means the learner reserves the right to revise this upper bound twice, and so on. A bound of ω 2 means that identification can be carried out by a learner that announces an upper bound on the number of times it may revise its conjectured upper bound on the number of mind changes. It is shown in the present paper that the ordinal mind change complexity for identification of languages formed by unions of up to n pattern languages is ω n. It is
A Generalization of the Least General Generalization
, 1994
"... In this chapter, we present a polynomial time algorithm, called a kminimal multiple generalization (kmmg) algorithm, where k 1, and its application to inductive learning problems. The algorithm is a natural extension of the least general generalization algorithm developed by Plotkin and Reynolds ..."
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Cited by 7 (5 self)
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In this chapter, we present a polynomial time algorithm, called a kminimal multiple generalization (kmmg) algorithm, where k 1, and its application to inductive learning problems. The algorithm is a natural extension of the least general generalization algorithm developed by Plotkin and Reynolds. Given a finite set of ground firstorder terms, the kmmg algorithm generalizes the examples by at most k firstorder terms, while Plotkin's algorithm does by a single firstorder term. We apply the kmmg algorithm to several learning problems in inductive logic programming, and knowledge discovery in databases. 1 Introduction Inductive inference is a process to guess or identify an unknown general rule from its examples. An inference algorithm receives finite examples and produces a generalization of them as a hypothesis. This paper concerns with inference only from positive examples. For example, recently, a number of studies are aimed at knowledge discovery in databases (PiatetskySha...
Inferring Pure ContextFree Languages from Positive Data
 ACTA CYBERNETICA
, 1997
"... We study the possibilities to infer pure contextfree langauges from positive data. We can show that while the whole class of pure contextfree languages is not inferable from positive data, it has interesting subclasses which have the desired inference property. We study uniform pure languages, i.e ..."
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Cited by 7 (0 self)
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We study the possibilities to infer pure contextfree langauges from positive data. We can show that while the whole class of pure contextfree languages is not inferable from positive data, it has interesting subclasses which have the desired inference property. We study uniform pure languages, i.e., languages generated by pure grammars obeying restrictions on the length of the right hand sides of their productions, and pure languages generated by deterministic pure grammars.
Synthesizing Learners Tolerating Computable Noisy Data
 In Proc. 9th International Workshop on Algorithmic Learning Theory, Lecture
, 1998
"... An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) generates a sequence of decision procedures defining the family. F. Stephan's model of noisy data is employed, in which, roughly, c ..."
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Cited by 6 (0 self)
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An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) generates a sequence of decision procedures defining the family. F. Stephan's model of noisy data is employed, in which, roughly, correct data crops up infinitely often, and incorrect data only finitely often. In a completely computable universe, all data sequences, even noisy ones, are computable. New to the present paper is the restriction that noisy data sequences be, nonetheless, computable! Studied, then, is the synthesis from indices for r.e. classes and for indexed families of languages of various kinds of noisetolerant languagelearners for the corresponding classes or families indexed, where the noisy input data sequences are restricted to being computable. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The main positive result is surpris...
A Polynomial Time Algorithm for Finding Finite Unions of Tree Pattern Languages
 In Proc. the 2nd NIL, LNAI 659
, 1993
"... A tree pattern is a structured pattern known as a term in formal logic, and a tree pattern language is the set of trees which are the ground instances of a tree pattern. In this paper, we deal with the class of tree languages whose language is defined as a union of at most k tree pattern languages, ..."
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Cited by 5 (4 self)
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A tree pattern is a structured pattern known as a term in formal logic, and a tree pattern language is the set of trees which are the ground instances of a tree pattern. In this paper, we deal with the class of tree languages whose language is defined as a union of at most k tree pattern languages, where k is an arbitrary fixed positive number. In particular, we present a polynomial time algorithm that, given a finite set of trees, to find a set of tree patterns that defines a minimal union of at most k tree pattern languages containing the given set. The algorithm can be considered as a natural extension of Plotkin's antiunification algorithm, which finds a minimal single tree pattern language containing the given set. By using the algorithm, we can realize a consistent and conservative polynomial time inference machine that identifies the class of unions of k tree pattern languages in the limit from positive data for every k ? 0. 1 Introduction Inductive inference is a process to ...
Polynomial Time Inference of A Subclass of Contextfree Transformations
 In Proceedings of the Fifth Workshop on Computational Learning Theory (COLT92
"... This paper deals with a class of Prolog programs, called contextfree term transformations (CFT). We present a polynomial time algorithm to identify a subclass of CFT, whose program consists of at most two clauses, from positive data; The algorithm uses 2mmg (2minimal multiple generalization) algor ..."
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Cited by 5 (2 self)
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This paper deals with a class of Prolog programs, called contextfree term transformations (CFT). We present a polynomial time algorithm to identify a subclass of CFT, whose program consists of at most two clauses, from positive data; The algorithm uses 2mmg (2minimal multiple generalization) algorithm, which is a natural extension of Plotkin's least generalization algorithm, to reconstruct the pair of heads of the unknown program. Using this algorithm, we show the consistent and conservative polynomial time identifiability of the class of tree languages defined by CFTFB uniq together with tree languages defined by pairs of two tree patterns, both of which are proper subclasses of CFT, in the limit from positive data. 1 Introduction The problem considered in this paper is, given an infinite sequence of facts which are true in the unknown model, to identify a Prolog program P that defines the unknown model M in the limit. We deal with the class CFTFB uniq of contextfree term transfor...
Extensional Set Learning
 Proceedings of The Twelfth Annual Conference on Computational Learning Theory (COLT '99
, 2000
"... We investigate the model recBC of learning of r.e. sets, where changes in hypotheses only count when there is an extensional difference. We study the learnability of collections that are uniformly r.e. We prove that, in contrast with the case of uniformly recursive collections, identifiability d ..."
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Cited by 4 (2 self)
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We investigate the model recBC of learning of r.e. sets, where changes in hypotheses only count when there is an extensional difference. We study the learnability of collections that are uniformly r.e. We prove that, in contrast with the case of uniformly recursive collections, identifiability does not imply recursive BCidentifiability. This answers a question of D. de Jongh. In contrast to the model of recursive identifiability, we prove that the BCmodel separates the notions of finite thickness and finite elasticity. 1 Introduction In this paper we consider a model of learning where two hypotheses about the data under consideration are considered equal when they denote the same object, i.e. when they are extensionally the same. This model was first defined for identification of functions in Feldman [6], Barzdin [3]. The first reference for this model in the context of set learning (learning from text) seems to be Osherson and Weinstein [14]. The model, and similar ones, ha...