Giorgio Picci – författare

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 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. These are new areas of rapid growth and of increasing importance in modern technology. The essays, written by world-leading experts in the field, reproduce and expand the plenary and minicoursejminisymposia invited lectures which were delivered at the Mathematical Theory of Networks and Systems Sym­ posium (MTNS-98), held in Padova, Italy, on July 6-10, 1998. Systems, control, and networks theory has permeated the development of much of present day technology. The impact has been visible in the past fifty years through the dramatic expansion and achievements of the aerospace and avionics industry, through process control and factory au­ tomation, robotics, communication signals analysis and synthesis, and, more recently, even finance, to name just the most visible applications. The theory has developed from the early phase of its history when the ba­ sic tools were elementary complex analysis, Laplace transform, and linear differential equations, to present day, where the mathematics ranges widely from functional analysis, PDE''s, abstract algebra, stochastic processes and differential geometry. Irrespective of the particular tools, however, the ba­ sic unifying paradigms of feedback, stability, optimal control, and recursive filtering, have remained the bulk of the field and continue to be the basic motivation for the theory, coming from the real world.

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.

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. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notionof the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory.