Probability And Statistics For Computer Scientists, Second Edition

This book was written for statisticians, computer scientists, geographers, researchers, and others interested in visualizing data. It presents a unique foundation for producing almost every quantitative graphic found in scientific journals, newspapers, statistical packages, and data visualization systems. While the tangible results of this work have been several visualization software libraries, this book focuses on the deep structures involved in producing quantitative graphics from data.

This book was written for statisticians, computer scientists, geographers, researchers, and others interested in visualizing data. It presents a unique foundation for producing almost every quantitative graphic found in scientific journals, newspapers, statistical packages, and data visualization systems. While the tangible results of this work have been several visualization software libraries, this book focuses on the deep structures involved in producing quantitative graphics from data.

Advances in computers and biotechnology have had a profound impact on biomedical research, and as a result complex data sets can now be generated to address extremely complex biological questions. Correspondingly, advances in the statistical methods necessary to analyze such data are following closely behind the advances in data generation methods. The statistical methods required by bioinformatics present many new and difficult problems for the research community.

The aim of this book is to discuss the fundamental ideas which lie behind the statistical theory of learning and generalization. It considers learning as a general problem of function estimation based on empirical data. Omitting proofs and technical details, the author concentrates on discussing the main results of learning theory and their connections to fundamental problems in statistics. These include: * the setting of learning problems based on the model of minimizing the risk functional from empirical data * a comprehensive analysis of the empirical risk minimization principle including necessary and sufficient conditions for its consistency * non-asymptotic bounds for the risk achieved using the empirical risk minimization principle * principles for controlling the generalization ability of learning machines using small sample sizes based on these bounds * the Support Vector methods that control the generalization ability when estimating function using small sample size.

by Marek Kimmel (Author), David Axelrod (Author)