Giorgio Picci - Böcker

This graduate textbook on the statistical approach to data science describes the basic ideas, scientific principles and common techniques for the extraction of mathematical models from observed data. Aimed at young scientists, and motivated by their scientific prospects, it provides first principle derivations of various algorithms and procedures, thereby supplying a solid background for their future specialization to diverse fields and applications.The beginning of the book presents the basics of statistical science, with an exposition on linear models. This is followed by an analysis of some numerical aspects and various regularization techniques, including LASSO, which are particularly important for large scale problems. Decision problems are studied both from the classical hypothesis testing perspective and, particularly, from a modern support-vector perspective, in the linear and non-linear context alike. Underlying the book is the Bayesian approach and the Bayesian interpretation of various algorithms and procedures. This is the key to principal components analysis and canonical correlation analysis, which are explained in detail. Following a chapter on nonlinear inference, including material on neural networks, the book concludes with a discussion on time series analysis and estimating their dynamic models.Featuring examples and exercises partially motivated by engineering applications, this book is intended for graduate students in applied mathematics and engineering with a general background in probability and linear algebra.

This book is a collection of essays devoted in part to new research direc­ tions in systems, networks, and control theory, and in part to the growing interaction of these disciplines with new sectors of engineering and applied sciences like coding, computer vision, and hybrid systems.

This book offers a tutorial view of recent trends in the science of modelling, adaptation, and learning. The most important modern approaches to identification, namely the stochastic, behavioral, subspace, and frequency domain approaches, are discussed thoroughly. On adaptation, tuning the parameters of a linear model is presented as a cure for uncertainty, and the asymptotics of recursive least squares and self-tuning systems are explained simply after a fully deterministic analysis. For constructing nonlinear models from data, neural networks and wavelets are considered as useful nonlinear tools, and fuzzy logic is presented as a way of coping with qualitative information. A final chapter deals with optimization methods. The book will become an important reference for researchers in the field.

This book offers a tutorial view of recent trends in the science of modelling, adaptation, and learning. The most important modern approaches to identification, namely the stochastic, behavioral, subspace, and frequency domain approaches, are discussed thoroughly. On adaptation, tuning the parameters of a linear model is presented as a cure for uncertainty, and the asymptotics of recursive least squares and self-tuning systems are explained simply after a fully deterministic analysis. For constructing nonlinear models from data, neural networks and wavelets are considered as useful nonlinear tools, and fuzzy logic is presented as a way of coping with qualitative information. A final chapter deals with optimization methods. The book will become an important reference for researchers in the field.

This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences.