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

2026-01-05

arXiv.org

AI Summary

This study addresses the severe computational bottleneck in detecting high-order epistatic interactions, which arises from combinatorial explosion. To overcome this challenge, the authors propose a novel approach that integrates Factorization Machines (FM) with quadratic optimization via simulated annealing, formulating the search for high-order interactions as a black-box optimization problem. The objective function is defined as the classification error rate of Multifactor Dimensionality Reduction (MDR), enabling efficient exploration of optimal genetic locus combinations within a limited number of iterations. The method substantially alleviates the computational complexity of conventional MDR in high-dimensional spaces and accurately identifies predefined epistatic patterns across multiple simulated datasets, demonstrating both efficiency and robustness under varying interaction orders and locus scales.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Search

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

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.

Problem

• high-order epistasis
• genetic association studies
• combinatorial explosion
• epistasis detection
• multifactor dimensionality reduction

Innovation

• Factorization Machine
• Quadratic Optimization Annealing
• High-Order Epistasis
• Multifactor Dimensionality Reduction
• Black-Box Optimization