KR2022Proceedings of the 19th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning

Haifa, Israel. July 31–August 5, 2022.

Edited by
  1. Gabriele Kern-Isberner
  2. Gerhard Lakemeyer
  3. Thomas Meyer

ISSN: 2334-1033
ISBN: 978-1-956792-01-0

Sponsored by
Published by

Copyright © 2022 International Joint Conferences on Artificial Intelligence Organization

Sum-Product Loop Programming: From Probabilistic Circuits to Loop Programming

  1. Viktor Pfanschilling(Computer Science Department, Technical University of Darmstadt, Germany)
  2. Hikaru Shindo(Computer Science Department, Technical University of Darmstadt, Germany)
  3. Devendra Singh Dhami(Computer Science Department, Technical University of Darmstadt, Germany, Hessian Center for AI, Darmstadt, Germany)
  4. Kristian Kersting(Computer Science Department, Technical University of Darmstadt, Germany, Center for Cognitive Science, Technical University of Darmstadt, Germany, Hessian Center for AI, Darmstadt, Germany)
PDF
BibTeX
https://doi.org/10.24963/kr.2022/47

Keywords

  1. Learning tractable probabilistic models
  2. Statistical relational learning
  3. Neural-symbolic learning
  4. Probabilistic reasoning and learning

Abstract

Recently, Probabilistic Circuits such as Sum-Product Networks have received growing attention, as they can represent complex features but still provide tractable inference. Although quite successful, unfortunately, they lack the capability of handling control structures, such as for and while loops. In this work, we introduce Sum-Product Loop Language (SPLL), a novel programming language that is capable of tractable inference on complex probabilistic code that includes loops.

SPLL has dual semantics: every program has generative semantics familiar to most programmers and

probabilistic semantics that assign a probability to each possible result. This way, the programmer can describe how to generate samples almost like in any standard programming language. The language takes care of computing the probability values of all results for free at run time.

We demonstrate that SPLL inherits the beneficial properties of PCs, namely tractability and differentiability, while generalizing to other distributions and programs, and retains substantial computational similarities.