Preface

Abstract

Probabilistic programsProbabilistic programs describe recipes for inferring statistical conclusions from a complex mixture of uncertain data and real-world observations.They can represent probabilistic graphical models far beyond the capabilities of Bayesian networks and are expected to have a major impact on machine intelligence.Probabilistic programs are ubiquitous.They steer autonomous robots and self-driving cars, are key to describe security mechanisms, naturally code up randomised algorithms for solving NP-hard or even unsolvable problems, and are rapidly encroaching on AI.Probabilistic programming aims to make probabilistic modelling and machine learning accessible to the programmer. What is this book all about?Probabilistic programs, though typically relatively small in size, are hard to grasp, let alone check automatically.Elementary questions are notoriously hard -even the most elementary question "does a program halt with probability one?-is "more undecidable" than the halting problem.This book is about the theoretical foundations of probabilistic programming.It is primarily concerned with fundamental questions such as the following: What is Bayesian probability theory?What is the precise mathematical meaning of probabilistic programs?How show almost-sure termination?How determine the (possibly infinite) expected runtime of probabilistic programs?How can two similar programs be compared?It covers several analysis techniques on probabilistic programs such as abstract interpretation, algebraic reasoning and determining concentration measures.These chapters are complemented with chapters on the formal definition of concrete probabilistic programming languages and some possible applications of the use of probabilistic programs.

Authors 3

1. Gilles Barthe

   Max Planck Institute for Security and Privacy

   Affiliation as printed

   Max Planck Institute for Security and Privacy

2. Joost-Pieter Katoen Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Germany

3. Alexandra Silva

   University College London

   Affiliation as printed

   University College London