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Foundations of Probabilistic Programming
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Book description

What does a probabilistic program actually compute? How can one formally reason about such probabilistic programs? This valuable guide covers such elementary questions and more. It provides a state-of-the-art overview of the theoretical underpinnings of modern probabilistic programming and their applications in machine learning, security, and other domains, at a level suitable for graduate students and non-experts in the field. In addition, the book treats the connection between probabilistic programs and mathematical logic, security (what is the probability that software leaks confidential information?), and presents three programming languages for different applications: Excel tables, program testing, and approximate computing. This title is also available as Open Access on Cambridge Core.

Reviews

'In our data-rich world, probabilistic programming is what allows programmers to perform statistical inference in a principled way for use in automated decision making. This rapidly growing field, which has emerged at the intersection of machine learning, statistics and programming languages, has the potential to become the driving force behind AI. But probabilistic programs can be counterintuitive and difficult to understand. This edited volume gives a comprehensive overview of the foundations of probabilistic programming, clearly elucidating the basic principles of how to design and reason about probabilistic programs, while at the same time highlighting pertinent applications and existing languages. With its breadth of topic coverage, the book will serve as an important and timely reference for researchers and practitioners.'

Marta Kwiatkowska - University of Oxford

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Contents

Full book PDF
  • Frontmatter
    pp i-iv
  • Contents
    pp v-vi
  • List of Contributors
    pp vii-x
  • Preface
    pp xi-xiv
  • 1 - Semantics of Probabilistic Programming: A Gentle Introduction
    pp 1-42
  • 2 - Probabilistic Programs as Measures
    pp 43-74
  • 3 - Application ofComputable Distributions to the Semantics of Probabilistic Programs
    pp 75-120
  • 4 - On Probabilistic λ-Calculi
    pp 121-144
  • 5 - Probabilistic Couplings from Program Logics
    pp 145-184
  • 6 - Expected Runtime Analyis by Program Verification
    pp 185-220
  • 7 - Termination Analysis of Probabilistic Programs with Martingales
    pp 221-258
  • 8 - Quantitative Analysis of Programs with Probabilities and Concentration of Measure Inequalities
    pp 259-294
  • 9 - The Logical Essentials of Bayesian Reasoning
    pp 295-332
  • 10 - Quantitative Equational Reasoning
    pp 333-360
  • 11 - Probabilistic Abstract Interpretation: Sound Inference and Application to Privacy
    pp 361-390
  • 12 - Quantitative Information Flow with Monads in Haskell
    pp 391-448
  • 13 - Luck: A Probabilistic Language for Testing
    pp 449-488
  • 14 - Tabular: Probabilistic Inference from the Spreadsheet
    pp 489-532
  • 15 - Programming Unreliable Hardware
    pp 533-568

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