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Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.

Stochastic processes --- Estimation theory --- Combinatorial analysis --- Distribution (Probability theory) --- 519.2 --- 519.21 --- 519.246 --- Combinatorics --- Algebra --- Mathematical analysis --- Estimating techniques --- Least squares --- Mathematical statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability. Mathematical statistics --- Probability theory. Stochastic processes --- Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- 519.246 Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- 519.21 Probability theory. Stochastic processes --- 519.2 Probability. Mathematical statistics --- Statistics . --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics

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Mathematical logic --- Complex analysis --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- complexe analyse (wiskunde) --- informatica --- wiskunde --- logica --- robots

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Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with highprobability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in a

Probabilities. --- Inequalities (Mathematics) --- Probabilités --- Inégalités (Mathématiques) --- Probabilities --- Processes, Infinite --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

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This book constitutes the refereed proceedings of the 20th International Conference on Algorithmic Learning Theory, ALT 2009, held in Porto, Portugal, in October 2009, co-located with the 12th International Conference on Discovery Science, DS 2009. The 26 revised full papers presented together with the abstracts of 5 invited talks were carefully reviewed and selected from 60 submissions. The papers are divided into topical sections of papers on online learning, learning graphs, active learning and query learning, statistical learning, inductive inference, and semisupervised and unsupervised learning. The volume also contains abstracts of the invited talks: Sanjoy Dasgupta, The Two Faces of Active Learning; Hector Geffner, Inference and Learning in Planning; Jiawei Han, Mining Heterogeneous; Information Networks By Exploring the Power of Links, Yishay Mansour, Learning and Domain Adaptation; Fernando C.N. Pereira, Learning on the Web.

Computer algorithms --- Machine learning --- Computer Science --- Mechanical Engineering - General --- Mechanical Engineering --- Engineering & Applied Sciences --- Information Technology --- Artificial Intelligence --- Computer science. --- Computer programming. --- Data mining. --- Information storage and retrieval. --- Artificial intelligence. --- Computational linguistics. --- Pattern recognition. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Programming Techniques. --- Data Mining and Knowledge Discovery. --- Language Translation and Linguistics. --- Pattern Recognition. --- Information Storage and Retrieval. --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Automatic language processing --- Language and languages --- Language data processing --- Linguistics --- Natural language processing (Linguistics) --- Applied linguistics --- Cross-language information retrieval --- Mathematical linguistics --- Multilingual computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Computers --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Informatics --- Science --- Data processing --- Programming --- Natural language processing (Computer science). --- Optical pattern recognition. --- Information storage and retrieva. --- Artificial Intelligence. --- Natural Language Processing (NLP). --- NLP (Computer science) --- Artificial intelligence --- Human-computer interaction --- Semantic computing --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Information storage and retrieval systems. --- Automatic data storage --- Automatic information retrieval --- Automation in documentation --- Computer-based information systems --- Data processing systems --- Data storage and retrieval systems --- Discovery systems, Information --- Information discovery systems --- Information processing systems --- Information retrieval systems --- Machine data storage and retrieval --- Mechanized information storage and retrieval systems --- Computer systems --- Electronic information resources --- Data libraries --- Digital libraries --- Information organization --- Information retrieval

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Mathematical statistics --- Computer science --- Information systems --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- Translation science --- Linguistics --- patroonherkenning --- IR (information retrieval) --- factoranalyse --- informatica --- vertalen --- linguïstiek --- database management --- KI (kunstmatige intelligentie) --- robots --- AI (artificiële intelligentie)