Foundations of Probabilistic Programming

Abstract

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.

Towards Abstraction-based Probabilistic Program Analysis

“…The upper part of the model is the chain from [3]. The parameters n and p can be chosen appropriately for any ε such that if standard value iteration is stopped when the latest change was smaller than ε, then the final approximation of the probability of reaching a target from s 0 is less than 5 8 , while the real probability is 1.…”

Automated Expected Amortised Cost Analysis of Probabilistic Data Structures

“…One of the main reasons for considering probabilistic models is that they often allow for the design of more efficient algorithms than their deterministic counterparts (see e.g. [6,23,25]). Another avenue for the design of efficient algorithms has been opened up by Sleator and Tarjan [34,36] with their introduction of the notion of amortised complexity.…”

The probabilistic termination tool amber

“…Probabilistic programming obviates the need to manually provide inference methods for different stochastic models and enables rapid prototyping [1,2]. Automated formal verification of probabilistic programs, however, is still in its infancy.…”