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128
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 ..."
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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.
Optimal Prefetching via Data Compression
, 1995
"... Caching and prefetching are important mechanisms for speeding up access time to data on secondary storage. Recent work in competitive online algorithms has uncovered several promising new algorithms for caching. In this paper we apply a form of the competitive philosophy for the first time to the pr ..."
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Cited by 236 (11 self)
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Caching and prefetching are important mechanisms for speeding up access time to data on secondary storage. Recent work in competitive online algorithms has uncovered several promising new algorithms for caching. In this paper we apply a form of the competitive philosophy for the first time to the problem of prefetching to develop an optimal universal prefetcher in terms of fault ratio, with particular applications to largescale databases and hypertext systems. Our prediction algorithms for prefetching are novel in that they are based on data compression techniques that are both theoretically optimal and good in practice. Intuitively, in order to compress data effectively, you have to be able to predict future data well, and thus good data compressors should be able to predict well for purposes of prefetching. We show for powerful models such as Markov sources and nth order Markov sources that the page fault rates incurred by our prefetching algorithms are optimal in the limit for almost all sequences of page requests.
Tracking the best expert
 In Proceedings of the 12th International Conference on Machine Learning
, 1995
"... Abstract. We generalize the recent relative loss bounds for online algorithms where the additional loss of the algorithm on the whole sequence of examples over the loss of the best expert is bounded. The generalization allows the sequence to be partitioned into segments, and the goal is to bound th ..."
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Cited by 198 (18 self)
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Abstract. We generalize the recent relative loss bounds for online algorithms where the additional loss of the algorithm on the whole sequence of examples over the loss of the best expert is bounded. The generalization allows the sequence to be partitioned into segments, and the goal is to bound the additional loss of the algorithm over the sum of the losses of the best experts for each segment. This is to model situations in which the examples change and different experts are best for certain segments of the sequence of examples. In the single segment case, the additional loss is proportional to log n, where n is the number of experts and the constant of proportionality depends on the loss function. Our algorithms do not produce the best partition; however the loss bound shows that our predictions are close to those of the best partition. When the number of segments is k +1and the sequence is of length ℓ, we can bound the additional loss of our algorithm over the best partition by O(k log n + k log(ℓ/k)). For the case when the loss per trial is bounded by one, we obtain an algorithm whose additional loss over the loss of the best partition is independent of the length of the sequence. The additional loss becomes O(k log n + k log(L/k)), where L is the loss of the best partition with k +1segments. Our algorithms for tracking the predictions of the best expert are simple adaptations of Vovk’s original algorithm for the single best expert case. As in the original algorithms, we keep one weight per expert, and spend O(1) time per weight in each trial.
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.
SCHAPIRE: Adaptive game playing using multiplicative weights
 Games and Economic Behavior
, 1999
"... We present a simple algorithm for playing a repeated game. We show that a player using this algorithm suffers average loss that is guaranteed to come close to the minimum loss achievable by any fixed strategy. Our bounds are nonasymptotic and hold for any opponent. The algorithm, which uses the mult ..."
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Cited by 134 (14 self)
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We present a simple algorithm for playing a repeated game. We show that a player using this algorithm suffers average loss that is guaranteed to come close to the minimum loss achievable by any fixed strategy. Our bounds are nonasymptotic and hold for any opponent. The algorithm, which uses the multiplicativeweight methods of Littlestone and Warmuth, is analyzed using the Kullback–Liebler divergence. This analysis yields a new, simple proof of the min–max theorem, as well as a provable method of approximately solving a game. A variant of our gameplaying algorithm is proved to be optimal in a very strong sense. Journal of Economic Literature
On the Generalization Ability of Online Learning Algorithms
 IEEE Transactions on Information Theory
, 2001
"... In this paper we show that online algorithms for classification and regression can be naturally used to obtain hypotheses with good datadependent tail bounds on their risk. Our results are proven without requiring complicated concentrationofmeasure arguments and they hold for arbitrary onlin ..."
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Cited by 133 (8 self)
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In this paper we show that online algorithms for classification and regression can be naturally used to obtain hypotheses with good datadependent tail bounds on their risk. Our results are proven without requiring complicated concentrationofmeasure arguments and they hold for arbitrary online learning algorithms. Furthermore, when applied to concrete online algorithms, our results yield tail bounds that in many cases are comparable or better than the best known bounds.
Regret in the Online Decision Problem
, 1999
"... At each point in time a decision maker must choose a decision. The payoff in a period from the decision chosen depends on the decision as well as the state of the world that obtains at that time. The difficulty is that the decision must be made in advance of any knowledge, even probabilistic, about ..."
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Cited by 115 (2 self)
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At each point in time a decision maker must choose a decision. The payoff in a period from the decision chosen depends on the decision as well as the state of the world that obtains at that time. The difficulty is that the decision must be made in advance of any knowledge, even probabilistic, about which state of the world will obtain. A range of problems from a variety of disciplines can be framed in this way. In this
A Deterministic Approach to Throughput Scaling in Wireless Networks
 Transactions on Information Theory
, 2004
"... Abstract—We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other ..."
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Cited by 115 (3 self)
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Abstract—We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bitmeters per second. We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the log throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting nonindependent and identically distributed (i.i.d.) node distributions are also provided. Index Terms—Ad hoc networks, capacity, deterministic, individual sequence, multihop, random, scaling, throughput, wireless networks. I.
LeZiUpdate: An InformationTheoretic Approach to Track Mobile Users in PCS Networks
, 1999
"... The complexity of the mobility tracking problem in a cellular environment has been characterized under an informationtheoretic framework. Shannon’s entropy measure is identified as a basis for comparing user mobility models. By building and maintaining a dictionary of individual user’s path update ..."
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Cited by 112 (12 self)
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The complexity of the mobility tracking problem in a cellular environment has been characterized under an informationtheoretic framework. Shannon’s entropy measure is identified as a basis for comparing user mobility models. By building and maintaining a dictionary of individual user’s path updates (as opposed to the widely used location updates), the proposed adaptive online algorithm can learn subscribers’ profiles. This technique evolves out of the concepts of lossless compression. The compressibility of the variabletofixed length encoding of the acclaimed LempelZiv family of algorithms reduces the update cost, whereas their builtin predictive power can be effectively used to reduce paging cost.
Variable Length Markov Chains
 Annals of Statistics
, 1999
"... We study estimation in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of higher order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary higher order Markov ..."
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Cited by 85 (5 self)
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We study estimation in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of higher order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary higher order Markov chains. From a more algorithmic view, the VLMC model class has attracted interest in information theory and machine learning but statistical properties have not been explored very much. Provided that good estimation is available, an additional structural richness of the model class enhances predictive power by finding a better tradeoff between model bias and variance and allows better structural description which can be of specific interest. The latter is exemplified with some DNA data. A version of the treestructured context algorithm, proposed by Rissanen (1983) in an information theoretical setup, is shown to have new good asymptotic properties for estimation in the class of VLMC's, even when the underlying model increases in dimensionality: consistent estimation of minimal state spaces and mixing properties of fitted models are given. We also propose a new bootstrap scheme based on fitted VLMC's. We show its validity for quite general stationary categorical time series and for a broad range of statistical procedures. AMS 1991 subject classifications. Primary 62M05; secondary 60J10, 62G09, 62M10, 94A15 Key words and phrases. Bootstrap, categorical time series, central limit theorem, context algorithm, data compression, finitememory sources, FSMX model, KullbackLeibler distance, model selection, tree model. Short title: Variable Length Markov Chain 1 Research supported in part by the Swiss National Science Foundation. Part of the work has been done while visiting th...