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important new text and reference for researchers and students in machine learning, game theory, statistics, and information theory offers the first comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class.  \nThe central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems are viewed as instances of the experts’ framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections. Old and new forecasting methods are described in a mathematically precise way in order to characterize their theoretical limitations and possibilities.  \nNicol Cesa-Bianchi is Professor of Computer Science at the University of Milan, Italy. His research interests include learning theory, pattern analysis, and worst-case analysis of algorithms. He is an action editor of the journal Machine Learning.  \nGbor Lugosi has been working on various problems in pattern classification, nonparametric statistics, statistical learning theory, game theory, probability, and information theory. He is coauthor of the monographs A Probabilistic Theory of Pattern Recognition and Combinatorial Methods of Density Estimation. He has been an associate editor of various journals, including the IEEE Transactions of Information Theory, Test, ESAIM: Probability and Statistics, and Statistics and Decisions.  \nPrediction, Learning, and Games  \nNICOLO` CESA-BIANCHI Universit degli Studi di Milano  \nGA´ BOR LUGOSI Universitat Pompeu Fabra, Barcelona  \ncambridge university press  \nCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo  \nCambridge University Press  \nThe Edinburgh Building, Cambridge cb2 2ru, UK  \nPublished in the United States of America by Cambridge University Press, New York [www.cambridge.org](www.cambridge.org)  \nInformation on this [title: www.cambridge.org/9780521841085](title: www.cambridge.org/9780521841085)  \n© Nicolo Cesa-Bianchi and Gabor Lugosi  \nThis publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.  \nFirst published in print format 2006  \nisbn-13 978-0-511-19178-7 eBook (NetLibrary)  \nisbn-10 0-511-19178-2 eBook (NetLibrary)  \nisbn-13 978-0-521-84108-5 hardback isbn-10 0-521-84108-9 hardback  \nCambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.  \nto Betta, Silvia, and Luca – NCB  \nto Arrate, Dani, and Frida to the memory of my parents – GL  \nContents  \nPreface page xi  \n1 Introduction 1  \n1.1 Prediction 1  \n1.2 Learning 3  \n1.3 Games 3  \n1.4 A Gentle Start 4  \n1.5 A Note to the Reader 6  \n2 Prediction with Expert Advice 7  \n2.1 Weighted Average Prediction 9  \n2.2 An Optimal Bound 15  \n2.3 Bounds That Hold Uniformly over Time 17  \n2.4 An Improvement for Small Losses 20  \n2.5 Forecasters Using the Gradient of the Loss 22  \n2.6 Scaled Losses and Signed Games 24  \n2.7 The Multilinear Forecaster 25  \n2.8 The Exponential Forecaster for Signed  \nGames 27  \n2.9 Simulatable Experts 29  \n2.10 Minimax Regret 30  \n2.11 Discounted Regret 32  \n2.12 Bibliographic Re","cbCaikA4rY2wdalr","https://ap.wps.com/l/cbCaikA4rY2wdalr","pdf",2376937,"English","# Preface\n# Introduction\n## Prediction\n## Learning\n## Games\n## A Gentle Start\n## A Note to the Reader\n# Prediction with Expert Advice\n## Weighted Average Prediction\n## An Optimal Bound\n## Bounds That Hold Uniformly over Time\n## An Improvement for Small Losses\n## Forecasters Using the Gradient of the Loss\n## Scaled Losses and Signed Games\n## The Multilinear Forecaster\n## The Exponential Forecaster for Signed Games\n## Simulatable Experts\n## Minimax Regret\n## Discounted Regret\n## Bibliographic Remarks\n## Exercises\n# Tight Bounds for Specific Losses\n## Follow the Best Expert\n## Exp-concave Loss Functions\n## The Greedy Forecaster\n## The Aggregating Forecaster\n## Mixability for Certain Losses\n## General Lower Bounds\n## Bibliographic Remarks\n## Exercises","[{\"question\":\"What makes prediction of individual sequences different from standard forecasting approaches?\",\"answer\":\"It does not impose probabilistic assumptions on the data-generating mechanism, yet constructs algorithms that perform nearly as well as the best strategy in a given reference class.\"},{\"question\":\"What is the central framework used to organize the book’s problems?\",\"answer\":\"The model of prediction using expert advice, which provides a general framework to cast and discuss multiple related problems from a nonstochastic standpoint.\"},{\"question\":\"Which kinds of problems are analyzed as instances of the experts’ framework?\",\"answer\":\"Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and other related problems.\"}]","Prediction, Learning, and Games - A Comprehensive Treatment of Individual Sequence Forecasting | PDF",1789975562,1026]