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979 results in Applied probability and stochastic networks

Page 3 of 49

  • 3 - Stochastic Gradient MCMC Algorithms

  • Paul Fearnhead, Lancaster University, Christopher Nemeth, Newcastle University, Chris J. Oates, University of Newcastle upon Tyne, Chris Sherlock, Lancaster University
  • Book:
    Scalable Monte Carlo for Bayesian Learning
    Published online:
    16 May 2025
    Print publication:
    05 June 2025, pp 62-102

  • Summary

    This chapter introduces stochastic gradient MCMC (SG-MCMC) algorithms, designed to scale Bayesian inference to large datasets. Beginning with the unadjusted Langevin algorithm (ULA), it extends to more sophisticated methods such as stochastic gradient Langevin dynamics (SGLD). The chapter emphasises controlling the stochasticity in gradient estimators and explores the role of control variates in reducing variance. Convergence properties of SG-MCMC methods are analysed, with experiments demonstrating their performance in logistic regression and Bayesian neural networks. It concludes by outlining a general framework for SG-MCMC and offering practical guidance for efficient, scalable Bayesian learning.

Partially Observed Markov Decision Processes
  • Filtering, Learning and Controlled Sensing
  • 2nd edition
  • Vikram Krishnamurthy
  • Published online:
    16 May 2025
    Print publication:
    05 June 2025
  • Covering formulation, algorithms and structural results and linking theory to real-world applications in controlled sensing (including social learning, adaptive radars and sequential detection), this book focuses on the conceptual foundations of partially observed Markov decision processes (POMDPs). It emphasizes structural results in stochastic dynamic programming, enabling graduate students and researchers in engineering, operations research, and economics to understand the underlying unifying themes without getting weighed down by mathematical technicalities. In light of major advances in machine learning over the past decade, this edition includes a new Part V on inverse reinforcement learning as well as a new chapter on non-parametric Bayesian inference (for Dirichlet processes and Gaussian processes), variational Bayes and conformal prediction.

Scalable Monte Carlo for Bayesian Learning
  • Paul Fearnhead, Christopher Nemeth, Chris J. Oates, Chris Sherlock
  • Published online:
    16 May 2025
    Print publication:
    05 June 2025
  • A graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC), as applied broadly in the Bayesian computational context. The topics covered have emerged as recently as the last decade and include stochastic gradient MCMC, non-reversible MCMC, continuous time MCMC, and new techniques for convergence assessment. A particular focus is on cutting-edge methods that are scalable with respect to either the amount of data, or the data dimension, motivated by the emerging high-priority application areas in machine learning and AI. Examples are woven throughout the text to demonstrate how scalable Bayesian learning methods can be implemented. This text could form the basis for a course and is sure to be an invaluable resource for researchers in the field.

Random Graphs and Complex Networks
  • Volume 2
  • Remco van der Hofstad
  • Published online:
    08 February 2024
    Print publication:
    08 February 2024
  • Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.

  • 8 - Small-World Phenomena in Preferential Attachment Models

  • from Part III - Small-World Properties of Random Graphs
  • Remco van der Hofstad, Technische Universiteit Eindhoven, The Netherlands
  • Book:
    Random Graphs and Complex Networks
    Published online:
    08 February 2024
    Print publication:
    08 February 2024, pp 326-380

  • Summary

    In this chapter we investigate graph distances in preferential attachment models. We focus on typical distances as well as the diameter of preferential attachment models. We again rely on path-counting techniques, as well as local limit results. Since the local limit is a rather involved quantity, some parts of our analysis are considerably harder than those in Chapters 6 and 7.

  • 7 - Small-World Phenomena in Configuration Models

  • from Part III - Small-World Properties of Random Graphs
  • Remco van der Hofstad, Technische Universiteit Eindhoven, The Netherlands
  • Book:
    Random Graphs and Complex Networks
    Published online:
    08 February 2024
    Print publication:
    08 February 2024, pp 289-325

  • Summary

    In this chapter we investigate the distance structure of the configuration model by investigating its typical distances and its diameter. We adapt the path-counting techniques in Chapter 6 to the configuration model, and obtain typical distances from the “giant is almost local” proof. To understand the ultra-small distances for infinite-variance degree configuration models, we investigate the generation growth of infinite-mean branching processes. The relation to branching processes informally leads to the power-iteration technique that allows one to deduce typical distance results in random graphs in a relatively straightforward way.

Page 3 of 49