---
title: "Handling Overlaps When Lifting Gaussian Bayesian Networks"
authors:
  - "Mattis Hartwig"
  - "Tanya Braun"
  - "Ralf Möller"
doi: "10.24963/ijcai.2021/581"
url: "https://ijcai.org/proceedings/2021/581"
pdf: "https://ijcai.org/proceedings/2021/0581.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "4228-4234"
track: "Main Track"
keywords:
  - "Uncertainty in AI: Bayesian Networks"
  - "Uncertainty in AI: Exact Probabilistic Inference"
  - "Uncertainty in AI: Statistical Relational AI"
  - "Uncertainty in AI: Graphical Models"
---

# Handling Overlaps When Lifting Gaussian Bayesian Networks

Mattis Hartwig, Tanya Braun, Ralf Möller

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 4228-4234. DOI: [10.24963/ijcai.2021/581](https://doi.org/10.24963/ijcai.2021/581)

## Abstract

Gaussian Bayesian networks are widely used for modeling the behavior of continuous random variables. Lifting exploits symmetries when dealing with large numbers of isomorphic random variables. It provides a more compact representation for more efficient query answering by encoding the symmetries using logical variables. This paper improves on an existing lifted representation of the joint distribution represented by a Gaussian Bayesian network (lifted joint), allowing overlaps between the logical variables. Handling overlaps without grounding a model is critical for modelling real-world scenarios.
Specifically, this paper contributes (i) a lifted joint that allows overlaps in logical variables and (ii) a lifted query answering algorithm using the lifted joint. Complexity analyses and experimental results show that - despite overlaps - constructing a lifted joint and answering queries on the lifted joint outperform their grounded counterparts significantly.