Sun 15 Jan 2023 10:20 - 10:30 at Scollay - First Session Chair(s): Steven Holtzen, Christine Tasson

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate computing. We explore the theory of generating functions and investigate its usage in the exact quantitative reasoning of probabilistic programs. Important topics include the exact representation of program semantics, proving exact program equivalence, and – as our main focus in this extended abstract – exact probabilistic inference.

In probabilistic programming, inference aims to derive a program’s posterior distribution. In contrast to approximate inference, inferring exact distributions comes with several benefits, e.g., no loss of precision, natural support for symbolic parameters, and efficiency on models with certain structures. Exact probabilistic inference, however, is a notoriously hard task. The challenges mainly arise from three program constructs: (1) unbounded while-loops and/or recursion, (2) infinite-support distributions, and (3) conditioning (via posterior observations). We present our ongoing research in addressing these challenges (with a focus on conditioning) leveraging generating functions and show their potential in facilitating exact probabilistic inference for discrete probabilistic programs.

Exact Probabilistic Inference Using Generating Functions (lafi23-final16.pdf)224KiB

Sun 15 Jan

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09:00 - 10:30
First SessionLAFI at Scollay
Chair(s): Steven Holtzen Northeastern University, Christine Tasson Sorbonne Université — LIP6
Day opening
Opening Comments
Christine Tasson Sorbonne Université — LIP6, Steven Holtzen Northeastern University
Introduction to the tensor-programs framework, a PL approach that helps analyse theoretical properties of deep learning.Boston
A: Hongseok Yang KAIST; IBS
Exact Inference for Discrete Probabilistic Programs via Generating FunctionsParis
A: Fabian Zaiser University of Oxford, C.-H. Luke Ong University of Oxford
File Attached
Exact Probabilistic Inference Using Generating FunctionsBoston
A: Lutz Klinkenberg RWTH Aachen University, Tobias Winkler RWTH Aachen University, Mingshuai Chen RWTH Aachen, Joost-Pieter Katoen RWTH Aachen University
File Attached