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Guaranteed Inference for Probabilistic Programs: A Parallelisable, Small-Step Operational Approach

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14500))

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Abstract

We put forward an approach to the semantics of probabilistic programs centered on an action-based language equipped with a small-step operational semantics. This approach provides benefits in terms of both clarity and effective implementation. Discrete and continuous distributions can be freely mixed, unbounded loops are allowed. In measure-theoretic terms, a product of Markov kernels is used to formalize the small-step operational semantics. This approach directly leads to an exact sampling algorithm that can be efficiently SIMD-parallelized. An observational semantics is also introduced based on a probability space of infinite sequences, along with a finite approximation theorem. Preliminary experiments with a proof-of-concept implementation based on TensorFlow show that our approach compares favourably to state-of-the-art tools for probabilistic programming and inference.

Work partially supported by the project SERICS (PE00000014) under the NRRP MUR program funded by the EU - NextGenerationEU.

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Notes

  1. 1.

    E.g. when multiple threads execute independent chains in a Markov Chain Monte Carlo method.

  2. 2.

    Variables \(x_i\) are only introduced as syntactic sugar: they will not get instantiated, and might be dispensed with using a terser notation, like \(@i=g\) and \(@i\sim G\).

  3. 3.

    Technically, Definition 2 requires that we specify a density \(\rho _G((c,2r),\cdot )\) also when \(r\le 0\): this can be fixed arbitrarily for our purposes.

  4. 4.

    For this example, we have used \(10^5\) samples. In fact, the stated bounds hold with very high probability: this will be made rigorous in the next section in terms of confidence intervals.

  5. 5.

    For instance, in Python via the Numpy or TensorFlow packages.

  6. 6.

    Like for algorithm \(\mathcal {A}\), since f is assumed to be the lifting of some h defined on \(\Omega \), we only keep the last element of each sequence, \(\omega _{i,t_0}\) in the notation of (13).

  7. 7.

    Our PC configuration is as follows. OS: Windows 10; CPU: 2.8 GHz Intel Core i7; GPU: Nvidia T500, driver v. 522.06; TF: v. 2.10.1; CUDA Toolkit v. 11.8; cuDNN SDK v. 8.6.0.

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Authors and Affiliations

  1. Dipartimento di Statistica, Informatica, Applicazioni “G. Parenti”, Università degli Studi di Firenze, Florence, Italy

    Michele Boreale & Luisa Collodi

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  1. Michele Boreale
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  2. Luisa Collodi
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Correspondence to Michele Boreale .

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Editors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Rayna Dimitrova

  2. Tel Aviv University, Tel Aviv, Israel

    Ori Lahav

  3. New York University, New York, NY, USA

    Sebastian Wolff

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Boreale, M., Collodi, L. (2024). Guaranteed Inference for Probabilistic Programs: A Parallelisable, Small-Step Operational Approach. In: Dimitrova, R., Lahav, O., Wolff, S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2024. Lecture Notes in Computer Science, vol 14500. Springer, Cham. https://doi.org/10.1007/978-3-031-50521-8_7

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  • DOI: https://doi.org/10.1007/978-3-031-50521-8_7

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  • Online ISBN: 978-3-031-50521-8

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