# High-Order Epistasis Detection Using Factorization Machine with Quadratic Optimization Annealing and MDR-Based Evaluation

arXiv: https://arxiv.org/abs/2601.01860 · HTML: https://mlsanity.com/paper/2601.01860/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 34 references that are in the map.
- First posted on arXiv 5 Jan 2026.

## Builds on (most cited first, 2 of 2)

- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [SWIFT-FMQA: Enhancing Factorization Machine with Quadratic-Optimization Annealing via Sliding Window](https://mlsanity.com/paper/2507.21024/) (2025)

## Built on by (most cited first, 1 of 1)

- [Factorization Machine with Quadratic-Optimization Annealing for RNA Inverse Folding and Evaluation of Binary-Integer Encoding and Nucleotide Assignment](https://mlsanity.com/paper/2602.16643/) (2026)

## Abstract (arXiv)

Detecting high-order epistasis is a fundamental challenge in genetic association studies due to the combinatorial explosion of candidate locus combinations. Although multifactor dimensionality reduction (MDR) is a widely used method for evaluating epistasis, exhaustive MDR-based searches become computationally infeasible as the number of loci or the interaction order increases. In this paper, we define the epistasis detection problem as a black-box optimization problem and solve it with a factorization machine with quadratic-optimization annealing (FMQA). We propose an efficient epistasis detection method based on FMQA, in which the classification error rate (CER) computed by MDR is used as a black-box objective function. Experimental evaluations were conducted using simulated case-control datasets with predefined high-order epistasis. The results demonstrate that the proposed method successfully identified ground-truth epistasis across various interaction orders and the numbers of genetic loci within a limited number of iterations. These results indicate that the proposed method is effective and computationally efficient for high-order epistasis detection.