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9096 results in Communications, Signal Processing and Information Theory

Page 35 of 455

Information-theoretic Cryptography
  • Himanshu Tyagi, Shun Watanabe
  • Published online:
    23 March 2023
    Print publication:
    13 April 2023
  • This book offers a mathematical foundation for modern cryptography. It is primarily intended as an introduction for graduate students. Readers should have basic knowledge of probability theory, but familiarity with computational complexity is not required. Starting from Shannon's classic result on secret key cryptography, fundamental topics of cryptography, such as secret key agreement, authentication, secret sharing, and secure computation, are covered. Particular attention is drawn to how correlated randomness can be used to construct cryptographic primitives. To evaluate the efficiency of such constructions, information-theoretic tools, such as smooth min/max entropies and information spectrum, are developed. The broad coverage means the book will also be useful to experts as well as students in cryptography as a reference for information-theoretic concepts and tools.

Inference and Learning from Data
  • Inference
  • Volume 2
  • Ali H. Sayed
  • Published online:
    17 March 2023
    Print publication:
    22 December 2022
  • This extraordinary three-volume work, written in an engaging and rigorous style by a world authority in the field, provides an accessible, comprehensive introduction to the full spectrum of mathematical and statistical techniques underpinning contemporary methods in data-driven learning and inference. This second volume, Inference, builds on the foundational topics established in volume I to introduce students to techniques for inferring unknown variables and quantities, including Bayesian inference, Monte Carlo Markov Chain methods, maximum-likelihood estimation, hidden Markov models, Bayesian networks, and reinforcement learning. A consistent structure and pedagogy is employed throughout this volume to reinforce student understanding, with over 350 end-of-chapter problems (including solutions for instructors), 180 solved examples, almost 200 figures, datasets and downloadable Matlab code. Supported by sister volumes Foundations and Learning, and unique in its scale and depth, this textbook sequence is ideal for early-career researchers and graduate students across many courses in signal processing, machine learning, statistical analysis, data science and inference.

  • 9 - Quotient manifolds

  • Nicolas Boumal, École Polytechnique Fédérale de Lausanne
  • Book:
    An Introduction to Optimization on Smooth Manifolds
    Published online:
    09 March 2023
    Print publication:
    16 March 2023, pp 205-251

  • Summary

    Optimization problems often have symmetries. For example, the value of the cost function may not change if its input vectors are scaled, translated or rotated. Then, it makes sense to quotient out the symmetries. If the quotient space is a manifold, it is called a quotient manifold. This often happens when the symmetries result from invariance to group actions: This chapter first reviews conditions for this to happen. Continuing with general quotient manifolds, the chapter reviews geometric concepts (points, tangent vectors, vector fields, retractions, Riemannian metrics, gradients, connections, Hessians and acceleration) to show how to work numerically with these abstract objects through lifts. The chapter aims to show the reader what it means to optimize on a quotient manifold, and how to do so on a computer. To this end, two important sections detail the relation between running Riemannian gradient descent and Newton’s method on the quotient manifold compared to running them on the non-quotiented manifold (called the total space). The running example is the Grassmann manifold as a quotient of the Stiefel manifold. Its tools are summarized in a closing section.

Page 35 of 455