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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  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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