Probability and Statistics for Computer Science

<p>This textbook is aimed at computer science undergraduates late in sophomore or early in junior year, supplying a comprehensive background in qualitative and quantitative data analysis, probability, random variables, and statistical methods, including machine learning.</p><p>With careful treatment of topics that fill the curricular needs for the course, <i>Probability and Statistics for Computer Science</i> features:<br></p><p>• A treatment of random variables and expectations dealing primarily with the discrete case.<br></p>• A practical treatment of simulation, showing how many interesting probabilities and expectations can be extracted, with particular emphasis on Markov chains.<p></p>• A clear but crisp account of simple point inference strategies (maximum likelihood; Bayesian inference) in simple contexts. This is extended to cover some confidence intervals, samples and populations for random sampling with replacement, and the simplest hypothesis testing.<p></p><p>• Achapter dealing with classification, explaining why it’s useful; how to train SVM classifiers with stochastic gradient descent; and how to use implementations of more advanced methods such as random forests and nearest neighbors.</p>• A chapter dealing with regression, explaining how to set up, use and understand linear regression and nearest neighbors regression in practical problems.<p></p>• A chapter dealing with principal components analysis, developing intuition carefully, and including numerous practical examples. There is a brief description of multivariate scaling via principal coordinate analysis.<p></p><p> </p><p>• A chapter dealing with clustering via agglomerative methods and k-means, showing how to build vector quantized features for complex signals.</p><p>Illustrated throughout, each main chapter includes many worked examples and other pedagogical elements such as </p>boxed Procedures, Definitions, Useful Facts, and Remember This (short tips). Problems and Programming Exercises are at the end of each chapter, with a summary of what the reader should know. <p></p>Instructor resources include a full set of model solutions for all problems, and an Instructor's Manual with accompanying presentation slides.<p></p>