Probabilistic Abstract Interpretation: Sound Inference and Application to Privacy. Jose Manuel Calderón Trilla, Michael Hicks, Stephen Magill, Piotr Mardziel, and Ian Sweet. In Gilles Barthe, Joost-Pieter Katoen, and Alexandra Silva, editors, Foundations of Probabilistic Programming, chapter 11, pages 361–389. Cambridge University Press, November 2020.

Bayesian probability models uncertain knowledge and learning from observations. As a defining feature of optimal adversarial behaviour, Bayesian reasoning forms the basis of safety properties in contexts such as privacy and fairness. Probabilistic programming is a convenient implementation of Bayesian reasoning but the adversarial setting imposes obstacles to its use: approximate inference can underestimate adversary knowledge and exact inference is impractical in cases covering large state spaces.

By abstracting distributions, the semantics of a probabilistic language, and inference, jointly termed probabilistic abstract interpretation, we demonstrate adversary models both approximate and sound.

We apply the techniques to build a privacy protecting monitor and describe how to trade off the precision and computational cost in its implementation all the while remaining sound with respect to privacy risk bounds.

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@incollection{trilla20probprog,
title = {Probabilistic Abstract Interpretation: Sound Inference and Application to Privacy},
booktitle = {Foundations of Probabilistic Programming},
author = {Jose Manuel Calder'{o}n Trilla and Michael Hicks and Stephen Magill and Piotr Mardziel and Ian Sweet},
editor = {Gilles Barthe and Joost-Pieter Katoen and Alexandra Silva},
chapter = 11,
pages = {361–389},
month = nov,
year = 2020,
publisher = {Cambridge University Press}
}

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