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63
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 93 (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
Minimum Description Length Induction, Bayesianism, and Kolmogorov Complexity
 IEEE Transactions on Information Theory
, 1998
"... The relationship between the Bayesian approach and the minimum description length approach is established. We sharpen and clarify the general modeling principles MDL and MML, abstracted as the ideal MDL principle and defined from Bayes's rule by means of Kolmogorov complexity. The basic conditi ..."
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Cited by 78 (8 self)
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The relationship between the Bayesian approach and the minimum description length approach is established. We sharpen and clarify the general modeling principles MDL and MML, abstracted as the ideal MDL principle and defined from Bayes's rule by means of Kolmogorov complexity. The basic condition under which the ideal principle should be applied is encapsulated as the Fundamental Inequality, which in broad terms states that the principle is valid when the data are random, relative to every contemplated hypothesis and also these hypotheses are random relative to the (universal) prior. Basically, the ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability, and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized. If we restrict the model class to the finite sets then application of the ideal principle turns into Kolmogorov's mi...
Learning Simple Concepts Under Simple Distributions
 SIAM JOURNAL OF COMPUTING
, 1991
"... We aim at developing a learning theory where `simple' concepts are easily learnable. In Valiant's learning model, many concepts turn out to be too hard (like NP hard) to learn. Relatively few concept classes were shown to be learnable polynomially. In daily life, it seems that things we ..."
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Cited by 57 (3 self)
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We aim at developing a learning theory where `simple' concepts are easily learnable. In Valiant's learning model, many concepts turn out to be too hard (like NP hard) to learn. Relatively few concept classes were shown to be learnable polynomially. In daily life, it seems that things we care to learn are usually learnable. To model the intuitive notion of learning more closely, we do not require that the learning algorithm learns (polynomially) under all distributions, but only under all simple distributions. A distribution is simple if it is dominated by an enumerable distrib...
Compression, Significance and Accuracy
, 1992
"... Inductive Logic Programming (ILP) involves learning relational concepts from examples and background knowledge. To date all ILP learning systems make use of tests inherited from propositional and decision tree learning for evaluating the significance of hypotheses. None of these significance t ..."
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Cited by 43 (5 self)
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Inductive Logic Programming (ILP) involves learning relational concepts from examples and background knowledge. To date all ILP learning systems make use of tests inherited from propositional and decision tree learning for evaluating the significance of hypotheses. None of these significance tests take account of the relevance or utility of the background knowledge. In this paper we describe a method, called HPcompression, of evaluating the significance of a hypothesis based on the degree to which it allows compression of the observed data with respect to the background knowledge. This can be measured by comparing the lengths of the input and output tapes of a reference Turing machine which will generate the examples from the hypothesis and a set of derivational proofs. The model extends an earlier approach of Muggleton by allowing for noise. The truth values of noisy instances are switched by making use of correction codes. The utility of compression as a significance measure is evaluated empirically in three independent domains. In particular, the results show that the existence of positive compression distinguishes a larger number of significant clauses than other significance tests The method is also shown to reliably distinguish artificially introduced noise as incompressible data.
Universal Algorithmic Intelligence: A mathematical topdown approach
 Artificial General Intelligence
, 2005
"... Artificial intelligence; algorithmic probability; sequential decision theory; rational ..."
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Cited by 30 (6 self)
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Artificial intelligence; algorithmic probability; sequential decision theory; rational
Towards a universal theory of artificial intelligence based on algorithmic probability and sequential decisions
 Proceedings of the 12 th Eurpean Conference on Machine Learning (ECML2001
, 2001
"... Abstract. Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental probability distribution is known. Solomonoff’s theory of universal induction formally solves the problem of sequence prediction for unknown distributions. We unify both theories an ..."
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Cited by 28 (10 self)
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Abstract. Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental probability distribution is known. Solomonoff’s theory of universal induction formally solves the problem of sequence prediction for unknown distributions. We unify both theories and give strong arguments that the resulting universal AIξ model behaves optimally in any computable environment. The major drawback of the AIξ model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIξ tl, which is still superior to any other time t and length l bounded agent. The computation time of AIξ tl is of the order t·2 l. 1
Distinguishing Exceptions from Noise in NonMonotonic Learning

, 1996
"... It is important for a learning program to have a reliable method of deciding whether to treat errors as noise or to include them as exceptions within a growing firstorder theory. We explore the use of an informationtheoretic measure to decide this problem within the nonmonotonic learning frame ..."
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Cited by 27 (2 self)
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It is important for a learning program to have a reliable method of deciding whether to treat errors as noise or to include them as exceptions within a growing firstorder theory. We explore the use of an informationtheoretic measure to decide this problem within the nonmonotonic learning framework defined by ClosedWorldSpecialisation. The approach adopted uses a model that consists of a reference Turing machine which accepts an encoding of a theory and proofs on its input tape and generates the observed data on the output tape. Within this model, the theory is said to "compress" data if the length of the input tape is shorter than that of the output tape. Data found to be incompressible are deemed to be "noise".
A Theory of Universal Artificial Intelligence based on Algorithmic Complexity
, 2000
"... Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ide ..."
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Cited by 26 (11 self)
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Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameterless theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline for a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning, how the AIXI model can formally solve them. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXItl, which is still effectively more intelligent than any other time t and space l bounded agent. The computation time of AIXItl is of the order t·2^l. Other discussed topics are formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.
Convergence and Error Bounds for Universal Prediction of Nonbinary Sequences
 Proceedings of the 12th Eurpean Conference on Machine Learning (ECML2001
, 2001
"... Solomonoff's uncomputable universal prediction scheme ß allows to predict the next symbol x k of a sequence x 1 ...x k1 for any Turing computable, but otherwise unknown, probabilistic environment µ . This scheme will be generalized to arbitrary environmental classes, which, ..."
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Cited by 22 (16 self)
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Solomonoff's uncomputable universal prediction scheme &szlig; allows to predict the next symbol x k of a sequence x 1 ...x k1 for any Turing computable, but otherwise unknown, probabilistic environment &micro; . This scheme will be generalized to arbitrary environmental classes, which, among others, allows the construction of computable universal prediction schemes &szlig; . Convergence of &szlig; to &micro; in a conditional mean squared sense and with &micro; probability 1 is proven. It is shown that the average number of prediction errors made by the universal &szlig; scheme rapidly converges to those made by the best possible informed &micro; scheme. The schemes, theorems and proofs are given for general finite alphabet, which results in additional complications as compared to the binary case. Several extensions of the presented theory and results are outlined. They include general loss functions and bounds, games of chance, infinite alphabet, partial and delayed prediction, classification, and more active systems.
New Error Bounds for Solomonoff Prediction
 Journal of Computer and System Sciences
, 1999
"... Several new relations between universal Solomonoff sequence prediction and informed prediction and general probabilistic prediction schemes will be proved. Among others, they show that the number of errors in Solomonoff prediction is finite for computable prior probability, if finite in the informed ..."
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Cited by 22 (16 self)
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Several new relations between universal Solomonoff sequence prediction and informed prediction and general probabilistic prediction schemes will be proved. Among others, they show that the number of errors in Solomonoff prediction is finite for computable prior probability, if finite in the informed case, where the prior is known. Deterministic variants will also be studied. The most interesting result is that the deterministic variant of Solomonoff prediction is optimal compared to any other probabilistic or deterministic prediction scheme apart from additive square root corrections only. This makes it well suited even for difficult prediction problems, where it does not suffice when the number of errors is minimal to within some factor greater than one. Solomonoff's original bound and the ones presented here complement each other in a useful way.