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How to Use Expert Advice
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1997
"... We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worstcase situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the ..."
Abstract

Cited by 317 (66 self)
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We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worstcase situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the algorithm by the difference between the expected number of mistakes it makes on the bit sequence and the expected number of mistakes made by the best expert on this sequence, where the expectation is taken with respect to the randomization in the predictions. We show that the minimum achievable difference is on the order of the square root of the number of mistakes of the best expert, and we give efficient algorithms that achieve this. Our upper and lower bounds have matching leading constants in most cases. We then show howthis leads to certain kinds of pattern recognition/learning algorithms with performance bounds that improve on the best results currently known in this context. We also compare our analysis to the case in which log loss is used instead of the expected number of mistakes.
Efficient Distributionfree Learning of Probabilistic Concepts
 Journal of Computer and System Sciences
, 1993
"... In this paper we investigate a new formal model of machine learning in which the concept (boolean function) to be learned may exhibit uncertain or probabilistic behaviorthus, the same input may sometimes be classified as a positive example and sometimes as a negative example. Such probabilistic c ..."
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Cited by 197 (8 self)
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In this paper we investigate a new formal model of machine learning in which the concept (boolean function) to be learned may exhibit uncertain or probabilistic behaviorthus, the same input may sometimes be classified as a positive example and sometimes as a negative example. Such probabilistic concepts (or pconcepts) may arise in situations such as weather prediction, where the measured variables and their accuracy are insufficient to determine the outcome with certainty. We adopt from the Valiant model of learning [27] the demands that learning algorithms be efficient and general in the sense that they perform well for a wide class of pconcepts and for any distribution over the domain. In addition to giving many efficient algorithms for learning natural classes of pconcepts, we study and develop in detail an underlying theory of learning pconcepts. 1 Introduction Consider the following scenarios: A meteorologist is attempting to predict tomorrow's weather as accurately as pos...
Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis
 IN PROCEEDINGS OF THE TWENTYSIXTH ANNUAL SYMPOSIUM ON THEORY OF COMPUTING
, 1994
"... We present new results on the wellstudied problem of learning DNF expressions. We prove that an algorithm due to Kushilevitz and Mansour [13] can be used to weakly learn DNF formulas with membership queries with respect to the uniform distribution. This is the rst positive result known for learn ..."
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Cited by 118 (23 self)
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We present new results on the wellstudied problem of learning DNF expressions. We prove that an algorithm due to Kushilevitz and Mansour [13] can be used to weakly learn DNF formulas with membership queries with respect to the uniform distribution. This is the rst positive result known for learning general DNF in polynomial time in a nontrivial model. Our results should be contrasted with those of Kharitonov [12], who proved that AC 0 is not eciently learnable in this model based on cryptographic assumptions. We also present ecient learning algorithms in various models for the readk and SATk subclasses of DNF. We then turn our attention to the recently introduced statistical query model of learning [9]. This model is a restricted version of the popular Probably Approximately Correct (PAC) model, and practically every PAC learning algorithm falls into the statistical query model [9]. We prove that DNF and decision trees are not even weakly learnable in polynomial time in this model. This result is informationtheoretic and therefore does not rely on any unproven assumptions, and demonstrates that no straightforward modication of the existing algorithms for learning various restricted forms of DNF and decision trees will solve the general problem. These lower bounds are a corollary of a more general characterization of the complexity of statistical query learning in terms of the number of uncorrelated functions in the concept class. The underlying tool for all of our results is the Fourier analysis of the concept class to be learned.
Provably BoundedOptimal Agents
 Journal of Artificial Intelligence Research
, 1995
"... Since its inception, artificial intelligence has relied upon a theoretical foundation centred around perfect rationality as the desired property of intelligent systems. We argue, as others have done, that this foundation is inadequate because it imposes fundamentally unsatisfiable requirements. As a ..."
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Cited by 79 (1 self)
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Since its inception, artificial intelligence has relied upon a theoretical foundation centred around perfect rationality as the desired property of intelligent systems. We argue, as others have done, that this foundation is inadequate because it imposes fundamentally unsatisfiable requirements. As a result, there has arisen a wide gap between theory and practice in AI, hindering progress in the field. We propose instead a property called bounded optimality. Roughly speaking, an agent is boundedoptimal if its program is a solution to the constrained optimization problem presented by its architecture and the task environment. We show how to construct agents with this property for a simple class of machine architectures in a broad class of realtime environments. We illustrate these results using a simple model of an automated mail sorting facility. We also define a weaker property, asymptotic bounded optimality (ABO), that generalizes the notion of optimality in classical complexity th...
Online algorithms in machine learning
 IN FIAT, AND WOEGINGER., EDS., ONLINE ALGORITHMS: THE STATE OF THE ART
, 1998
"... The areas of OnLine Algorithms and Machine Learning are both concerned with problems of making decisions about the present based only on knowledge of the past. Although these areas differ in terms of their emphasis and the problems typically studied, there are a collection of results in Computation ..."
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Cited by 61 (2 self)
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The areas of OnLine Algorithms and Machine Learning are both concerned with problems of making decisions about the present based only on knowledge of the past. Although these areas differ in terms of their emphasis and the problems typically studied, there are a collection of results in Computational Learning Theory that fit nicely into the "online algorithms" framework. This survey article discusses some of the results, models, and open problems from Computational Learning Theory that seem particularly interesting from the point of view of online algorithms. The emphasis in this article is on describing some of the simpler, more intuitive results, whose proofs can be given in their entirity. Pointers to the literature are given for more sophisticated versions of these algorithms.
Bayesian model averaging
 STAT.SCI
, 1999
"... Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to overcon dent inferences and decisions tha ..."
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Cited by 42 (0 self)
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Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to overcon dent inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA) provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA haverecently emerged. We discuss these methods and present anumber of examples. In these examples, BMA provides improved outofsample predictive performance. We also provide a catalogue of
Probabilistic Analysis of Learning in Artificial Neural Networks: The PAC Model and its Variants
, 1997
"... There are a number of mathematical approaches to the study of learning and generalization in artificial neural networks. Here we survey the `probably approximately correct' (PAC) model of learning and some of its variants. These models provide a probabilistic framework for the discussion of generali ..."
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Cited by 18 (4 self)
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There are a number of mathematical approaches to the study of learning and generalization in artificial neural networks. Here we survey the `probably approximately correct' (PAC) model of learning and some of its variants. These models provide a probabilistic framework for the discussion of generalization and learning. This survey concentrates on the sample complexity questions in these models; that is, the emphasis is on how many examples should be used for training. Computational complexity considerations are briefly discussed for the basic PAC model. Throughout, the importance of the VapnikChervonenkis dimension is highlighted. Particular attention is devoted to describing how the probabilistic models apply in the context of neural network learning, both for networks with binaryvalued output and for networks with realvalued output.
Text Data Mining with Optimized Pattern Discovery
 In Proc. 17th Workshop on Machine Intelligence
, 2000
"... This paper describes an application of the optimized pattern discovery framework to text and Web mining. In particular, weintroduce a class of simple combinatorial patterns over phrases, called proximity phrase association patterns, and consider the problem of #nding the patterns that optimizes a ..."
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Cited by 2 (0 self)
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This paper describes an application of the optimized pattern discovery framework to text and Web mining. In particular, weintroduce a class of simple combinatorial patterns over phrases, called proximity phrase association patterns, and consider the problem of #nding the patterns that optimizes a given statistical measure in a large collection of unstructured texts. For this class of patterns, we develop fast and robust text mining algorithms based on techniques from computational geometry and string matching. Then, we made experiments on large collections of documents and on Web pages to evaluate the proposed method. 1 Introduction The rapid progress of computer and network technologies makes it easy to collect and store a large amount of unstructured or semistructured texts suchaswebpages, HTML#XML archives, emails, and text #les. These text data can be thought of large scale text databases, and thus it becomes important to develop an e#cient tools to discover interesting kn...
Computational Learning Theory
"... Introduction Since the late fifties, computer scientists (particularly those working in the area of artificial intelligence) have been trying to understand how to construct computer programs that perform tasks we normally think of as requiring human intelligence, and which can improve their perform ..."
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Introduction Since the late fifties, computer scientists (particularly those working in the area of artificial intelligence) have been trying to understand how to construct computer programs that perform tasks we normally think of as requiring human intelligence, and which can improve their performance over time by modifying their behavior in response to experience. In other words, one objective has been to design computer programs that can learn. For example, Samuels designed a program to play checkers in the early sixties that could improve its performance as it gained experience playing against human opponents. More recently, research on artificial neural networks has stimulated interest in the design of systems capable of performing tasks that are difficult to describe algorithmically (such as recognizing a spoken word or identifying an object in a complex scene), by exposure to many examples. As a concrete example consider the task of handwritten character recognition.
Produced as part of the ESPRIT Working Group in Neural and Computational Learning II,
, 1998
"... We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use ..."
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We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use