Science & Mathematics - High-Dimensional Probability: An Introduction with Applications in Data Science (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 47)

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High-Dimensional Probability: An Introduction with Applications in Data Science (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 47)

Name: High-Dimensional Probability: An Introduction with Applications in Data Science (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 47)
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Book Synopsis: High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.

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Unlock the limitless potential of high-dimensional probability with the groundbreaking book, High-Dimensional Probability: An Introduction with Applications in Data Science. Combining the power of probability, analysis, and geometry, this comprehensive guide will revolutionize your understanding of random vectors, matrices, and subspaces in high dimensions. Whether you're a mathematician, statistician, or data scientist, this book is an invaluable resource for advancing your knowledge and expanding your horizons in the field.

With its integration of theory, key tools, and modern applications, High-Dimensional Probability is a game-changer. Master the core concept of concentration inequalities and gain access to both classic results and cutting-edge developments. Discover the groundbreaking matrix Bernstein's inequality and explore the potential of stochastic processes in high-dimensional probability. Unleash the power of tools like Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension.

High-Dimensional Probability is not just a theoretical exploration; it is accompanied by a wealth of real-life illustrations that showcase its versatility. From covariance estimation and clustering to machine learning and compressed sensing, this book covers a wide range of applications. Whether you're interested in network analysis, coding theory, dimension reduction, or sparse regression, this book has you covered.

Don't miss out on this groundbreaking guide to high-dimensional probability. Elevate your understanding, enhance your skills, and discover the endless possibilities of data science. Order your copy of High-Dimensional Probability: An Introduction with Applications in Data Science today and embark on a journey of mathematical and statistical discovery like never before.

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