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Probabilistic Approaches to Recommendations

The importance of accurate recommender systems has been widely recognized by academia and industry, and recommendation is rapidly becoming one of the most successful applications of data mining and machine learning. Understanding and predicting the choices and preferences of users is a challenging task: real-world scenarios involve users behaving in complex situations, where prior beliefs, specific tendencies, and reciprocal influences jointly contribute to determining the preferences of users toward huge amounts of information, services, and products. Probabilistic modeling represents a robust formal mathematical framework to model these assumptions and study their effects in the recommendation process. This book starts with a brief summary of the recommendation problem and its challenges and a review of some widely used techniques Next, we introduce and discuss probabilistic approaches for modeling preference data. We focus our attention on methods based on latent factors, such as mixture models, probabilistic matrix factorization, and topic models, for explicit and implicit preference data. These methods represent a significant advance in the research and technology of recommendation. The resulting models allow us to identify complex patterns in preference data, which can be exploited to predict future purchases effectively. The extreme sparsity of preference data poses serious challenges to the modeling of user preferences, especially in the cases where few observations are available. Bayesian inference techniques elegantly address the need for regularization, and their integration with latent factor modeling helps to boost the performances of the basic techniques. We summarize the strengths and weakness of several approaches by considering two different but related evaluation perspectives, namely, rating prediction and recommendation accuracy. Furthermore, we describe how probabilistic methods based on latent factors enable the exploitation of preference patterns in novel applications beyond rating prediction or recommendation accuracy. We finally discuss the application of probabilistic techniques in two additional scenarios, characterized by the availability of side information besides preference data. In summary, the book categorizes the myriad probabilistic approaches to recommendations and provides guidelines for their adoption in real-world situations.

An Introduction to Multivariable Mathematics

The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. The core material of the book is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in the first ten or eleven lectures, followed by a similar number of lectures on basic multivariable analysis, including first theorems on differentiable functions on domains in Euclidean space and a brief introduction to submanifolds. The book then concludes with further essential linear algebra, including the theory of determinants, eigenvalues, and the spectral theorem for real symmetric matrices, and further multivariable analysis, including the contraction mapping principle and the inverse and implicit function theorems. There is also an appendix which provides a nine-lecture introduction to real analysis. There are various ways in which the additional material in the appendix could be integrated into a course--for example in the Stanford Mathematics honors program, run as a four-lecture per week program in the Autumn Quarter each year, the first six lectures of the nine-lecture appendix are presented at the rate of one lecture per week in weeks two through seven of the quarter, with the remaining three lectures per week during those weeks being devoted to the main chapters of the text. It is hoped that the text would be suitable for a quarter or semester course for students who have scored well in the BC Calculus advanced placement examination (or equivalent), particularly those who are considering a possible major in mathematics. The author has attempted to make the presentation rigorous and complete, with the clarity and simplicity needed to make it accessible to an appropriately large group of students. Table of Contents: Linear Algebra / Analysis in R / More Linear Algebra / More Analysis in R / Appendix: Introductory Lectures on Real Analysis

The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis.

Single Molecule Biophysics and Poisson Process Approach to Statistical Mechanics

This is an overview of single molecule physics, the study of both equilibrium and non-equilibrium properties at the single molecule level. It begins with an introduction to this fascinating science and includes a chapter on how to build the most popular instrument for single molecule biophysics, the total internal reflection fluorescence (TIRF) microscope. It concludes with the Poisson process approach to statistical mechanics, explaining how to relate the process to diverse areas and see how data analysis and error bars are integral parts of science.

This is an overview of single molecule physics, the study of both equilibrium and non-equilibrium properties at the single molecule level.

Essentials of Applied Mathematics for Scientists and Engineers

This is a book about linear partial differential equations that are common in engineering and the physical sciences. It will be useful to graduate students and advanced undergraduates in all engineering fields as well as students of physics, chemistry, geophysics and other physical sciences and professional engineers who wish to learn about how advanced mathematics can be used in their professions. The reader will learn about applications to heat transfer, fluid flow, mechanical vibrations. The book is written in such a way that solution methods and application to physical problems are emphasized. There are many examples presented in detail and fully explained in their relation to the real world. References to suggested further reading are included. The topics that are covered include classical separation of variables and orthogonal functions, Laplace transforms, complex variables and Sturm-Liouville transforms.

It will be useful to graduate students and advanced undergraduates in all
engineering fields as well as students of physics, chemistry, geophysics and
other physical sciences and professional engineers who wish to learn about how
advanced ...

Essentials of Applied Mathematics for Engineers and Scientists

The Second Edition of this popular book on practical mathematics for engineers includes new and expanded chapters on perturbation methods and theory. This is a book about linear partial differential equations that are common in engineering and the physical sciences. It will be useful to graduate students and advanced undergraduates in all engineering ?elds as well as students of physics, chemistry, geophysics and other physical sciences and professional engineers who wish to learn about how advanced mathematics can be used in their professions. The reader will learn about applications to heat transfer, fluid flow and mechanical vibrations. The book is written in such a way that solution methods and application to physical problems are emphasized. There are many examples presented in detail and fully explained in their relation to the real world. References to suggested further reading are included. The topics that are covered include classical separation of variables and orthogonal functions, Laplace transforms, complex variables and Sturm-Liouville transforms. This second edition includes two new and revised chapters on perturbation methods, and singular perturbation theory of differential equations. Table of Contents: Partial Differential Equations in Engineering / The Fourier Method: Separation of Variables / Orthogonal Sets of Functions / Series Solutions of Ordinary Differential Equations / Solutions Using Fourier Series and Integrals / Integral Transforms: The Laplace Transform / Complex Variables and the Laplace Inversion Integral / Solutions with Laplace Transforms / Sturm-Liouville Transforms / Introduction to Perturbation Methods / Singular Perturbation Theory of Differential Equations / Appendix A: The Roots of Certain Transcendental Equations

It will be useful to graduate students and advanced undergraduates in all
engineering ?elds as well as students of physics, chemistry, geophysics and
other physical sciences and professional engineers who wish to learn about how
advanced ...

Active Learning

The key idea behind active learning is that a machine learning algorithm can perform better with less training if it is allowed to choose the data from which it learns. An active learner may pose "queries," usually in the form of unlabeled data instances to be labeled by an "oracle" (e.g., a human annotator) that already understands the nature of the problem. This sort of approach is well-motivated in many modern machine learning and data mining applications, where unlabeled data may be abundant or easy to come by, but training labels are difficult, time-consuming, or expensive to obtain. This book is a general introduction to active learning. It outlines several scenarios in which queries might be formulated, and details many query selection algorithms which have been organized into four broad categories, or "query selection frameworks." We also touch on some of the theoretical foundations of active learning, and conclude with an overview of the strengths and weaknesses of these approaches in practice, including a summary of ongoing work to address these open challenges and opportunities. Table of Contents: Automating Inquiry / Uncertainty Sampling / Searching Through the Hypothesis Space / Minimizing Expected Error and Variance / Exploiting Structure in Data / Theory / Practical Considerations

Machine learning is the study of computer systems that improve through
experience. Active learning is the study of machine learning systems that improve
by asking questions. So why ask questions? (Good question.) The key
hypothesis is ...

Dependency Parsing

Dependency-based methods for syntactic parsing have become increasingly popular in natural language processing in recent years. This book gives a thorough introduction to the methods that are most widely used today. After an introduction to dependency grammar and dependency parsing, followed by a formal characterization of the dependency parsing problem, the book surveys the three major classes of parsing models that are in current use: transition-based, graph-based, and grammar-based models. It continues with a chapter on evaluation and one on the comparison of different methods, and it closes with a few words on current trends and future prospects of dependency parsing. The book presupposes a knowledge of basic concepts in linguistics and computer science, as well as some knowledge of parsing methods for constituency-based representations. Table of Contents: Introduction / Dependency Parsing / Transition-Based Parsing / Graph-Based Parsing / Grammar-Based Parsing / Evaluation / Comparison / Final Thoughts

Dependency-based methods for syntactic parsing have become increasingly popular in natural language processing in recent years. This book gives a thorough introduction to the methods that are most widely used today.