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41
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.
Idleness is Not Sloth
, 1995
"... Many people have observed that computer systems spend much of their time idle, and various schemes have been proposed to use this idle time productively. The commonest approach is to offload activity from busy periods to lessbusy ones in order to improve system responsiveness. In addition, specula ..."
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Cited by 153 (9 self)
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Many people have observed that computer systems spend much of their time idle, and various schemes have been proposed to use this idle time productively. The commonest approach is to offload activity from busy periods to lessbusy ones in order to improve system responsiveness. In addition, speculative work can be performed in idle periods in the hopes that it will be needed later at times of higher utilization, or nonrenewable resource like battery power can be conserved by disabling unused resources. We found opportunities to exploit idle time in our work on storage systems, and after a few attempts to tackle specific instances of it in ad hoc ways, began to investigate general mechanisms that could be applied to this problem. Our results include a taxonomy of idletime detection algorithms, metrics for evaluating them, and an evaluation of a number of idleness predictors that we generated from our taxonomy. 1. Introduction Resource usage is often bursty: periods of high utilizat...
Universal prediction
 IEEE Transactions on Information Theory
, 1998
"... Abstract — This paper consists of an overview on universal prediction from an informationtheoretic perspective. Special attention is given to the notion of probability assignment under the selfinformation loss function, which is directly related to the theory of universal data compression. Both th ..."
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Cited by 136 (11 self)
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Abstract — This paper consists of an overview on universal prediction from an informationtheoretic perspective. Special attention is given to the notion of probability assignment under the selfinformation loss function, which is directly related to the theory of universal data compression. Both the probabilistic setting and the deterministic setting of the universal prediction problem are described with emphasis on the analogy and the differences between results in the two settings. Index Terms — Bayes envelope, entropy, finitestate machine, linear prediction, loss function, probability assignment, redundancycapacity, stochastic complexity, universal coding, universal prediction. I.
A Game of Prediction with Expert Advice
 Journal of Computer and System Sciences
, 1997
"... We consider the following problem. At each point of discrete time the learner must make a prediction; he is given the predictions made by a pool of experts. Each prediction and the outcome, which is disclosed after the learner has made his prediction, determine the incurred loss. It is known that, u ..."
Abstract

Cited by 106 (7 self)
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We consider the following problem. At each point of discrete time the learner must make a prediction; he is given the predictions made by a pool of experts. Each prediction and the outcome, which is disclosed after the learner has made his prediction, determine the incurred loss. It is known that, under weak regularity, the learner can ensure that his cumulative loss never exceeds cL+ a ln n, where c and a are some constants, n is the size of the pool, and L is the cumulative loss incurred by the best expert in the pool. We find the set of those pairs (c; a) for which this is true.
MistakeDriven Learning in Text Categorization
 IN EMNLP97, THE SECOND CONFERENCE ON EMPIRICAL METHODS IN NATURAL LANGUAGE PROCESSING
, 1997
"... Learning problems in the text processing domain often map the text to a space whose dimensions are the measured fea tures of the text, e.g., its words. Three characteristic properties of this domain are (a) very high dimensionality, (b) both the learned concepts and the instances reside very ..."
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Cited by 97 (9 self)
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Learning problems in the text processing domain often map the text to a space whose dimensions are the measured fea tures of the text, e.g., its words. Three characteristic properties of this domain are (a) very high dimensionality, (b) both the learned concepts and the instances reside very sparsely in the feature space, and (c) a high variation in the number of active features in an instance. In this work we study three mistakedriven learning algo rithms for a typical task of this nature  text categorization. We argue
A WinnowBased Approach to ContextSensitive Spelling Correction
 Machine Learning
, 1999
"... A large class of machinelearning problems in natural language require the characterization of linguistic context. Two characteristic properties of such problems are that their feature space is of very high dimensionality, and their target concepts depend on only a small subset of the features in th ..."
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Cited by 86 (1 self)
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A large class of machinelearning problems in natural language require the characterization of linguistic context. Two characteristic properties of such problems are that their feature space is of very high dimensionality, and their target concepts depend on only a small subset of the features in the space. Under such conditions, multiplicative weightupdate algorithms such as Winnow have been shown to have exceptionally good theoretical properties. In the work reported here, we present an algorithm combining variants of Winnow and weightedmajority voting, and apply it to a problem in the aforementioned class: contextsensitive spelling correction. This is the task of fixing spelling errors that happen to result in valid words, such as substituting to for too, casual for causal, and so on. We evaluate our algorithm, WinSpell, by comparing it against BaySpell, a statisticsbased method representing the state of the art for this task. We find: (1) When run with a full (unpruned) set ...
Sequential Prediction of Individual Sequences Under General Loss Functions
 IEEE Transactions on Information Theory
, 1998
"... We consider adaptive sequential prediction of arbitrary binary sequences when the performance is evaluated using a general loss function. The goal is to predict on each individual sequence nearly as well as the best prediction strategy in a given comparison class of (possibly adaptive) prediction st ..."
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Cited by 75 (7 self)
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We consider adaptive sequential prediction of arbitrary binary sequences when the performance is evaluated using a general loss function. The goal is to predict on each individual sequence nearly as well as the best prediction strategy in a given comparison class of (possibly adaptive) prediction strategies, called experts. By using a general loss function, we generalize previous work on universal prediction, forecasting, and data compression. However, here we restrict ourselves to the case when the comparison class is finite. For a given sequence, we define the regret as the total loss on the entire sequence suffered by the adaptive sequential predictor, minus the total loss suffered by the predictor in the comparison class that performs best on that particular sequence. We show that for a large class of loss functions, the minimax regret is either \Theta(log N) or \Omega\Gamma p ` log N ), depending on the loss function, where N is the number of predictors in the comparison class a...
Tracking the Best Disjunction
 Machine Learning
, 1995
"... . Littlestone developed a simple deterministic online learning algorithm for learning kliteral disjunctions. This algorithm (called Winnow) keeps one weight for each of the n variables and does multiplicative updates to its weights. We develop a randomized version of Winnow and prove bounds for a ..."
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Cited by 74 (11 self)
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. Littlestone developed a simple deterministic online learning algorithm for learning kliteral disjunctions. This algorithm (called Winnow) keeps one weight for each of the n variables and does multiplicative updates to its weights. We develop a randomized version of Winnow and prove bounds for an adaptation of the algorithm for the case when the disjunction may change over time. In this case a possible target disjunction schedule T is a sequence of disjunctions (one per trial) and the shift size is the total number of literals that are added/removed from the disjunctions as one progresses through the sequence. We develop an algorithm that predicts nearly as well as the best disjunction schedule for an arbitrary sequence of examples. This algorithm that allows us to track the predictions of the best disjunction is hardly more complex than the original version. However the amortized analysis needed for obtaining worstcase mistake bounds requires new techniques. In some cases our low...
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.
A secondorder perceptron algorithm
, 2005
"... Kernelbased linearthreshold algorithms, such as support vector machines and Perceptronlike algorithms, are among the best available techniques for solving pattern classification problems. In this paper, we describe an extension of the classical Perceptron algorithm, called secondorder Perceptr ..."
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Cited by 59 (21 self)
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Kernelbased linearthreshold algorithms, such as support vector machines and Perceptronlike algorithms, are among the best available techniques for solving pattern classification problems. In this paper, we describe an extension of the classical Perceptron algorithm, called secondorder Perceptron, and analyze its performance within the mistake bound model of online learning. The bound achieved by our algorithm depends on the sensitivity to secondorder data information and is the best known mistake bound for (efficient) kernelbased linearthreshold classifiers to date. This mistake bound, which strictly generalizes the wellknown Perceptron bound, is expressed in terms of the eigenvalues of the empirical data correlation matrix and depends on a parameter controlling the sensitivity of the algorithm to the distribution of these eigenvalues. Since the optimal setting of this parameter is not known a priori, we also analyze two variants of the secondorder Perceptron algorithm: one that adaptively sets the value of the parameter in terms of the number of mistakes made so far, and one that is parameterless, based on pseudoinverses.