# Variable Elimination in the Fourier Domain

arXiv: https://arxiv.org/abs/1508.04032 · HTML: https://mlsanity.com/paper/1508.04032/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2015.

## Built on by (most cited first, 2 of 2)

- [Polynomial Semantics of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2402.09085/) (2024)
- [Combining Local Symmetry Exploitation and Reinforcement Learning for Optimised Probabilistic Inference -- A Work In Progress](https://mlsanity.com/paper/2503.08786/) (2025)

## Abstract (arXiv)

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major computational advantages. We explore a different type of compact representation based on discrete Fourier representations, complementing the classical approach based on conditional independencies. We show that a large class of probabilistic graphical models have a compact Fourier representation. This theoretical result opens up an entirely new way of approximating a probability distribution. We demonstrate the significance of this approach by applying it to the variable elimination algorithm. Compared with the traditional bucket representation and other approximate inference algorithms, we obtain significant improvements.