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176
Learning Stochastic Logic Programs
, 2000
"... Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic contextfree grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a firstorder range ..."
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Cited by 1057 (71 self)
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Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic contextfree grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a firstorder rangerestricted definite clause. This paper summarises the syntax, distributional semantics and proof techniques for SLPs and then discusses how a standard Inductive Logic Programming (ILP) system, Progol, has been modied to support learning of SLPs. The resulting system 1) nds an SLP with uniform probability labels on each definition and nearmaximal Bayes posterior probability and then 2) alters the probability labels to further increase the posterior probability. Stage 1) is implemented within CProgol4.5, which differs from previous versions of Progol by allowing userdefined evaluation functions written in Prolog. It is shown that maximising the Bayesian posterior function involves nding SLPs with short derivations of the examples. Search pruning with the Bayesian evaluation function is carried out in the same way as in previous versions of CProgol. The system is demonstrated with worked examples involving the learning of probability distributions over sequences as well as the learning of simple forms of uncertain knowledge.
Computational Limitations on Learning from Examples
 Journal of the ACM
, 1988
"... Abstract. The computational complexity of learning Boolean concepts from examples is investigated. It is shown for various classes of concept representations that these cannot be learned feasibly in a distributionfree sense unless R = NP. These classes include (a) disjunctions of two monomials, (b) ..."
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Cited by 192 (10 self)
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Abstract. The computational complexity of learning Boolean concepts from examples is investigated. It is shown for various classes of concept representations that these cannot be learned feasibly in a distributionfree sense unless R = NP. These classes include (a) disjunctions of two monomials, (b) Boolean threshold functions, and (c) Boolean formulas in which each variable occurs at most once. Relationships between learning of heuristics and finding approximate solutions to NPhard optimization problems are given. Categories and Subject Descriptors: F. 1.1 [Computation by Abstract Devices]: Models of Computationrelations among models; F. 1.2 [Computation by Abstract Devices]: Modes of Computationprobabilistic computation; F. 1.3 [Computation by Abstract Devices]: Complexity Classesreducibility and completeness; 1.2.6 [Artificial Intelligence]: Learningconcept learning; induction
Inductive Inference, DFAs and Computational Complexity
 2nd Int. Workshop on Analogical and Inductive Inference (AII
, 1989
"... This paper surveys recent results concerning the inference of deterministic finite automata (DFAs). The results discussed determine the extent to which DFAs can be feasibly inferred, and highlight a number of interesting approaches in computational learning theory. 1 ..."
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Cited by 78 (1 self)
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This paper surveys recent results concerning the inference of deterministic finite automata (DFAs). The results discussed determine the extent to which DFAs can be feasibly inferred, and highlight a number of interesting approaches in computational learning theory. 1
Biometric identification
 Communications of the ACM
, 2000
"... Identification of grammars (r. e. indices) for recursively enumerable languages from positive data by algorithmic devices is a well studied problem in learning theory. The present paper considers identification of r. e. languages by machines that have access to membership oracles for noncomputable s ..."
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Cited by 60 (4 self)
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Identification of grammars (r. e. indices) for recursively enumerable languages from positive data by algorithmic devices is a well studied problem in learning theory. The present paper considers identification of r. e. languages by machines that have access to membership oracles for noncomputable sets. It is shown that for any set A there exists another set B such that the collections of r. e. languages that can be identified by machines with access to a membership oracle for B is strictly larger than the collections of r. e. languages that can be identified by machines with access to a membership oracle for A. In other words, there is no maximal inference degree for language identification.
The Power of Vacillation in Language Learning
, 1992
"... Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are ..."
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Cited by 44 (11 self)
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Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are classes of languages that can be learned if convergence in the limit to up to (n+1) exactly correct grammars is allowed but which cannot be learned if convergence in the limit is to no more than n grammars, where the no more than n grammars can each make finitely many mistakes. This contrasts sharply with results of Barzdin and Podnieks and, later, Case and Smith, for learnability from both positive and negative data. A subset principle from a 1980 paper of Angluin is extended to the vacillatory and other criteria of this paper. This principle, provides a necessary condition for circumventing overgeneralization in learning from positive data. It is applied to prove another theorem to the eff...
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
Beyond the Turing Test
 J. Logic, Language & Information
"... Abstract. We define the main factor of intelligence as the ability to comprehend, formalising this ability with the help of new constructs based on descriptional complexity. The result is a comprehension test, or Ctest, exclusively defined in terms of universal descriptional machines (e.g universal ..."
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Cited by 33 (18 self)
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Abstract. We define the main factor of intelligence as the ability to comprehend, formalising this ability with the help of new constructs based on descriptional complexity. The result is a comprehension test, or Ctest, exclusively defined in terms of universal descriptional machines (e.g universal Turing machines). Despite the absolute and nonanthropomorphic character of the test it is equally applicable to both humans and machines. Moreover, it correlates with classical psychometric tests, thus establishing the first firm connection between information theoretic notions and traditional IQ tests. The Turing Test is compared with the Ctest and their joint combination is discussed. As a result, the idea of the Turing Test as a practical test of intelligence should be left behind, and substituted by computational and factorial tests of different cognitive abilities, a much more useful approach for artificial intelligence progress and for many other intriguing questions that are presented beyond the Turing Test.
On the Structure of Degrees of Inferability
 Journal of Computer and System Sciences
, 1993
"... Degrees of inferability have been introduced to measure the learning power of inductive inference machines which have access to an oracle. The classical concept of degrees of unsolvability measures the computing power of oracles. In this paper we determine the relationship between both notions. ..."
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Cited by 32 (19 self)
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Degrees of inferability have been introduced to measure the learning power of inductive inference machines which have access to an oracle. The classical concept of degrees of unsolvability measures the computing power of oracles. In this paper we determine the relationship between both notions. 1 Introduction We consider learning of classes of recursive functions within the framework of inductive inference [21]. A recent theme is the study of inductive inference machines with oracles ([8, 10, 11, 17, 24] and tangentially [12]; cf. [10] for a comprehensive introduction and a collection of all previous results.) The basic question is how the information content of the oracle (technically: its Turing degree) relates with its learning power (technically: its inference degreedepending on the underlying inference criterion). In this paper a definitive answer is obtained for the case of recursively enumerable oracles and the case when only finitely many queries to the oracle are allo...
Incremental Learning from Positive Data
 Journal of Computer and System Sciences
, 1996
"... The present paper deals with a systematic study of incremental learning algorithms. ..."
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Cited by 32 (19 self)
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The present paper deals with a systematic study of incremental learning algorithms.
Language Learning from Texts: Mind Changes, Limited Memory and Monotonicity (Extended Abstract)
 INFORMATION AND COMPUTATION
, 1995
"... The paper explores language learning in the limit under various constraints on the number of mindchanges, memory, and monotonicity. We define language learning with limited (long term) memory and prove that learning with limited memory is exactly the same as learning via set driven machines (when t ..."
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Cited by 26 (9 self)
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The paper explores language learning in the limit under various constraints on the number of mindchanges, memory, and monotonicity. We define language learning with limited (long term) memory and prove that learning with limited memory is exactly the same as learning via set driven machines (when the order of the input string is not taken into account). Further we show that every language learnable via a set driven machine is learnable via a conservative machine (making only justifiable mindchanges). We get a variety of separation results for learning with bounded number of mindchanges or limited memory under restrictions on monotonicity. Many separation results have a variant: If a criterion A can be separated from B, then often it is possible to find a family L of languages such that L is A and B learnable, but while it is possible to restrict the number of mindchanges or long term memory...