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This chapter gives basic information about molecular communication. It introduces the concept and gives simple examples, explores the history of molecular communication, and discusses several examples to motivate the rest of the book.
Chapter 1 discusses the motivation for the book and the rationale for its organization into four parts: preliminary considerations, evaluation for classification, evaluation in other settings, and evaluation from a practical perspective. In more detail, the first part provides the statistical tools necessary for evaluation and reviews the main machine learning principles as well as frequently used evaluation practices. The second part discusses the most common setting in which machine learning evaluation has been applied: classification. The third part extends the discussion to other paradigms such as multi-label classification, regression analysis, data stream mining, and unsupervised learning. The fourth part broadens the conversation by moving it from the laboratory setting to the practical setting, specifically discussing issues of robustness and responsible deployment.
The book starts out with a motivating chapter to answer the question: Why is it worthwhile to develop system theory? To do so, we jump fearlessly in the very center of our methods, using a simple and straight example in optimization: optimal tracking. Although optimization is not our leading subject– which is system theory– it provides for one of the main application areas, namely the optimization of the performance of a dynamical system in a time-variant environment (for example, driving a car or sending a rocket to the moon). The chapter presents a recursive matrix algebra approach to the optimization problem, known as dynamic programming. Optimal tracking is based on a powerful principle called “dynamic programming,” which lies at the very basis of what ”dynamical” means.
The increased interest that the topic of critical infrastructure resilience is attracting in academia, government, commerce, services, and industry is creating an alternative engineering field that could be called resilience engineering. However, the views of the meaning of resilience have varied, and even in some very relevant world languages, an exact translation of the word “resilience” has only recently been introduced – for example, the word “resiliencia” was added to the dictionary of the Royal Academy of Spanish Language in 2014 – or it still does not exist, as happens in Japanese. Thus, this chapter introduces the main concepts associated with the study of resilience engineering applicable to critical infrastructure systems with a focus on electric power grids and information and communication networks (ICNs) because these are the infrastructures that are identified as “uniquely critical” in US Presidential Policy Directive 21, which is the source for the definition of resilience that is used in this book.
Edited by
Jong Chul Ye, Korea Advanced Institute of Science and Technology (KAIST),Yonina C. Eldar, Weizmann Institute of Science, Israel,Michael Unser, École Polytechnique Fédérale de Lausanne
We provide a short, self-contained introduction to deep neural networks that is aimed at mathematically inclined readers. We promote the use of a vect--matrix formalism that is well suited to the compositional structure of these networks and that facilitates the derivation/description of the backpropagation algorithm. We present a detailed analysis of supervised learning for the two most common scenarios, (i) multivariate regression and (ii) classification, which rely on the minimization of least squares and cross-entropy criteria, respectively.
Optimization on Riemannian manifolds–the result of smooth geometry and optimization merging into one elegant modern framework–spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing.
This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade sprinkled throughout the book for conducting research in this area and for writing effective numerical implementations.
Bayesian optimization is a methodology for optimizing expensive objective functions that has proven success in the sciences, engineering, and beyond. This timely text provides a self-contained and comprehensive introduction to the subject, starting from scratch and carefully developing all the key ideas along the way. This bottom-up approach illuminates unifying themes in the design of Bayesian optimization algorithms and builds a solid theoretical foundation for approaching novel situations.
The core of the book is divided into three main parts, covering theoretical and practical aspects of Gaussian process modeling, the Bayesian approach to sequential decision making, and the realization and computation of practical and effective optimization policies.
Following this foundational material, the book provides an overview of theoretical convergence results, a survey of notable extensions, a comprehensive history of Bayesian optimization, and an extensive annotated bibliography of applications.
It provides a brief description of the classical adaptive filtering algorithms, starting with defining the actual objective function each algorithm minimizes. It also includes a summary of the expected performance according to available results from the literature.
Edited by
Yonina C. Eldar, Weizmann Institute of Science, Israel,Andrea Goldsmith, Princeton University, New Jersey,Deniz Gündüz, Imperial College of Science, Technology and Medicine, London,H. Vincent Poor, Princeton University, New Jersey
This chapter discusses the fundamentally different mental images of large-dimensional machine learning (versus its small-dimensional counterpart), through the examples of sample covariance matrices and kernel matrices, on both synthetic and real data. Random matrix theory is presented as a flexible and powerful tool to assess, understand, and improve classical machine learning methods in this modern large-dimensional setting.