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66
Universal intelligence: A definition of machine intelligence
 Minds and Machines
, 2007
"... A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of ..."
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Cited by 42 (11 self)
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A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.
On Universal Prediction and Bayesian Confirmation
 Theoretical Computer Science
, 2007
"... The Bayesian framework is a wellstudied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not ..."
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Cited by 22 (13 self)
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The Bayesian framework is a wellstudied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not always available or can fail, in particular in complex situations. Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. I discuss in breadth how and in which sense universal (noni.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. I show that Solomonoff’s model possesses many desirable properties: Strong total and future bounds, and weak instantaneous bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the oldevidence and updating problem. It even performs well
Feature reinforcement learning: Part I. Unstructured MDPs
 Journal of General Artificial Intelligence
, 2009
"... www.hutter1.net Generalpurpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and nonMarkovian. On the other hand, reinforcement learning is welldeveloped for small finite state Markov decision processes (MDPs). Up ..."
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Cited by 16 (7 self)
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www.hutter1.net Generalpurpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and nonMarkovian. On the other hand, reinforcement learning is welldeveloped for small finite state Markov decision processes (MDPs). Up to now, extracting the right state representations out of bare observations, that is, reducing the general agent setup to the MDP framework, is an art that involves significant effort by designers. The primary goal of this work is to automate the reduction process and thereby significantly expand the scope of many existing reinforcement learning algorithms and the agents that employ them. Before we can think of mechanizing this search for suitable MDPs, we need a formal objective criterion. The main contribution of this article is to develop such a criterion. I also integrate the various parts into one learning algorithm. Extensions to more realistic dynamic Bayesian networks are developed in Part
Bayes not Bust! Why Simplicity is no Problem for Bayesians
, 2007
"... The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike’s Information Criterion (AIC), a nonBayesian formalisation of the notion of simplicity. ..."
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Cited by 13 (10 self)
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The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike’s Information Criterion (AIC), a nonBayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallace’s Minimum Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1to1 reparametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster’s objections to Bayesianism. Hence an important part of the attack on
Suboptimal behavior of Bayes and MDL in classification under misspecification
 COLT
, 2004
"... We show that forms of Bayesian and MDL inference that are often applied to classification problems can be inconsistent. This means that there exists a learning problem such that for all amounts of data the generalization errors of the MDL classifier and the Bayes classifier relative to the Bayesian ..."
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Cited by 13 (3 self)
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We show that forms of Bayesian and MDL inference that are often applied to classification problems can be inconsistent. This means that there exists a learning problem such that for all amounts of data the generalization errors of the MDL classifier and the Bayes classifier relative to the Bayesian posterior both remain bounded away from the smallest achievable generalization error. From a Bayesian point of view, the result can be reinterpreted as saying that Bayesian inference can be inconsistent under misspecification, even for countably infinite models. We extensively discuss the result from both a Bayesian and an MDL perspective.
A Philosophical Treatise of Universal Induction
 Entropy 2011
"... Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more ..."
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Cited by 11 (7 self)
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Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent theoretical results and is based on solid philosophical foundations, the requisite technical knowledge necessary for understanding this framework has caused it to remain largely unknown and unappreciated in the wider scientific community. The main contribution of this article is to convey Solomonoff induction and its related concepts in a generally accessible form with the aim of bridging this current technical gap. In the process we examine the major historical contributions that have led to the formulation of Solomonoff Induction as well as criticisms of Solomonoff and induction in general. In particular we examine how Solomonoff induction addresses many issues that have plagued other inductive systems, such as the black ravens paradox and the confirmation problem, and compare this approach with other recent approaches.
On the foundations of universal sequence prediction
 In Proc. 3rd Annual Conference on Theory and Applications of Models of Computation (TAMC’06), volume 3959 of LNCS
, 2006
"... Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (noni.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequenc ..."
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Cited by 11 (3 self)
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Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (noni.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. We show that Solomonoff’s model possesses many desirable properties: Fast convergence and strong bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the oldevidence and updating problem. It even performs well (actually better) in noncomputable environments.
MML Inference of Oblique Decision Trees
 In Lecture Notes in Artificial Intelligence (LNAI) 3339 (Springer), Proc. 17th Australian Joint Conf. on AI
, 2004
"... Abstract. We propose a multivariate decision tree inference scheme by using the minimum message length (MML) principle (Wallace and Boulton, 1968; Wallace and Dowe, 1999). The scheme uses MML coding as an objective (goodnessoffit) function on model selection and searches with a simple evolution st ..."
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Cited by 9 (5 self)
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Abstract. We propose a multivariate decision tree inference scheme by using the minimum message length (MML) principle (Wallace and Boulton, 1968; Wallace and Dowe, 1999). The scheme uses MML coding as an objective (goodnessoffit) function on model selection and searches with a simple evolution strategy. We test our multivariate tree inference scheme on UCI machine learning repository data sets and compare with the decision tree programs C4.5 and C5. The preliminary results show that on average and on most datasets, MML oblique trees clearly perform better than both C4.5 and C5 on both “right”/“wrong ” accuracy and probabilistic prediction and with smaller trees, i.e., less leaf nodes. 1
Causal models as minimal descriptions of multivariate systems. http://parallel.vub.ac.be/∼jan
, 2006
"... ABSTRACT. By applying the minimality principle for model selection, one should seek the model that describes the data by a code of minimal length. Learning is viewed as data compression that exploits the regularities or qualitative properties found in the data, in order to build a model containing t ..."
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Cited by 8 (0 self)
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ABSTRACT. By applying the minimality principle for model selection, one should seek the model that describes the data by a code of minimal length. Learning is viewed as data compression that exploits the regularities or qualitative properties found in the data, in order to build a model containing the meaningful information. The theory of causal modeling can be interpreted by this approach. The regularities are the conditional independencies reducing a factorization and the vstructure regularities. In the absence of other regularities, a causal model is faithful and offers a minimal description of a probability distribution. The causal interpretation of a faithful Bayesian network is motivated by the canonical representation it offers and faithfulness. A causal model decomposes the distribution into independent atomic blocks and is able to explain all qualitative properties found in the data. The existence of faithful models depends on the additional regularities in the data. Local structure of the conditional probability distributions allow further compression of the model. Interfering regularities, however, generate conditional independencies that do not follow from the Markov condition. These regularities has to be incorporated into an augmented model for which the inference algorithms are adapted to take into account their influences. But for other regularities, like patterns in a string, causality does not offer a modeling framework that leads to a minimal description. 1