Algebraic Statistics in OSCAR

2026-01-22

AI Summary

This work addresses the inefficiency of algebraic statistical computations and the difficulty of sharing results in computer algebra systems by designing and implementing a scalable algebraic statistics module within the OSCAR system. The module employs a modular architecture, integrates state-of-the-art implicitization algorithms to enhance computational efficiency, and introduces a standardized data serialization mechanism to enable cross-platform sharing of results and facilitate the construction of large-scale databases. By doing so, the project not only strengthens OSCAR’s functional completeness in algebraic statistics but also provides essential infrastructure for reproducible research and collaborative workflows, significantly improving the practicality and scalability of algebraic statistical methods.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Statistical Relational/Logic Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We introduce the AlgebraicStatistics section of the OSCAR computer algebra system. We give an overview of its extensible design and highlight its features including serialization of data types for sharing results and creating databases, and state-of-the-art implicitization algorithms.

Problem

• Algebraic Statistics
• Computer Algebra System
• OSCAR
• Data Serialization
• Implicitization

Innovation

• Algebraic Statistics
• OSCAR
• extensible design
• serialization
• implicitization algorithms