Verifying Sampling Algorithms via Distributional Invariants

2025-09-08

AI Summary

Discrete probabilistic sampling algorithms lack formal verification frameworks. Method: This paper proposes the first verification methodology based on *distributional loop invariants*: probabilistic programs are modeled as distribution transformers, and a Hoare-style logic is developed to support both total and partial correctness proofs. Contribution/Results: The key innovation is the systematic introduction of *distributional loop invariants*, enabling precise characterization and inductive reasoning about the evolution of output distributions during program execution. The framework unifies probabilistic program semantics, invariant inference, and formal verification techniques. Experimentally, it successfully verifies the correctness of two classic algorithms—Fast Dice Roller and Fast Loaded Dice Roller—demonstrating strong expressive power and practical applicability. This work establishes a novel paradigm for formal verification of probabilistic programs.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Logic Programming

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

This paper develops a verification framework aimed at establishing the correctness of discrete sampling algorithms. We do so by considering probabilistic programs as distribution transformers. Inspired by recent work on distributional verification of Markov models, we introduce the notion of (inductive) distributional loop invariants for discrete probabilistic programs. These invariants are embedded in a Hoare-like verification framework that includes proof rules for total and partial correctness. To illustrate the applicability of our framework, we prove the correctness of two discrete sampling algorithms: the Fast Dice Roller and the Fast Loaded Dice Roller.

Problem

• Verifying correctness of discrete sampling algorithms
• Developing Hoare-like framework with distributional invariants
• Proving correctness of Fast Dice Roller algorithms

Innovation

• Distributional loop invariants for probabilistic programs
• Hoare-like verification framework with proof rules
• Correctness proofs for discrete sampling algorithms