This volume is the outcome of a series of three lectures on statistical learning theory given at Institute Henri Poincaré in 2011 under the auspices of the Société Mathéatique de France. The introductory chapter provides an overview of the history of Statistical Learning Theory, its roots, and its mathematical tools. The chapter Algorithms for minimally supervised learning, by Sanjoy Dasgupta, describes the progress of theoretical computer science on the issues of unsupervised learning (clustering) and active learning. Surprisingly, much of this progress is due to the confrontation of measurement concentration theory, complexity theory, and established practices in numerical statistics. The chapter Online prediction, by Peter Bartlett, focuses on online learning. It is a confrontation between statistics, game theory and optimization. Information for our distributors: A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. AMS individual members receive a 10% discount and members of the SMF receive a 30% discount from list. No other discounts apply.
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Gregory F. Lawler, University of Chicago, IL.
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Paperback. Zustand: New. The title Random Explorations has two meanings. First, a few topics of advanced probability are deeply explored. Second, there is a recurring theme of analyzing a random object by exploring a random path.This book is an outgrowth of lectures by the author in the University of Chicago Research Experiences for Undergraduate (REU) program in 2020. The idea of the course was to expose advanced undergraduates to ideas in probability research.The book begins with Markov chains with an emphasis on transient or killed chains that have finite Green's function. This function, and its inverse called the Laplacian, is discussed next to relate two objects that arise in statistical physics, the loop-erased random walk (LERW) and the uniform spanning tree (UST). A modern approach is used including loop measures and soups. Understanding these approaches as the system size goes to infinity requires a deep understanding of the simple random walk so that is studied next, followed by a look at the infinite LERW and UST. Another model, the Gaussian free field (GFF), is introduced and related to loop measure. The emphasis in the book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution (SLE), and the continuous Gaussian free field. A number of exercises scattered throughout the text will help a serious reader gain better understanding of the material. Bestandsnummer des Verkäufers LU-9781470467661
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Paperback. Zustand: new. Paperback. The title Random Explorations has two meanings. First, a few topics of advanced probability are deeply explored. Second, there is a recurring theme of analyzing a random object by exploring a random path.This book is an outgrowth of lectures by the author in the University of Chicago Research Experiences for Undergraduate (REU) program in 2020. The idea of the course was to expose advanced undergraduates to ideas in probability research.The book begins with Markov chains with an emphasis on transient or killed chains that have finite Green's function. This function, and its inverse called the Laplacian, is discussed next to relate two objects that arise in statistical physics, the loop-erased random walk (LERW) and the uniform spanning tree (UST). A modern approach is used including loop measures and soups. Understanding these approaches as the system size goes to infinity requires a deep understanding of the simple random walk so that is studied next, followed by a look at the infinite LERW and UST. Another model, the Gaussian free field (GFF), is introduced and related to loop measure. The emphasis in the book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution (SLE), and the continuous Gaussian free field. A number of exercises scattered throughout the text will help a serious reader gain better understanding of the material. The emphasis of this book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution, and the continuous Gaussian free field. A number of exercises scattered throughout the text will help gain a better understanding of the material. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9781470467661
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