Inferring Higher-Order Couplings with Neural Networks

Area of Science:

• Statistical Physics
• Machine Learning
• Bioinformatics
• Neuroscience

Background:

• Maximum entropy methods infer pairwise interactions in complex systems but miss higher-order effects.
• Existing machine learning models capture higher-order interactions but are computationally expensive.
• Restricted Boltzmann Machines (RBMs) offer an efficient alternative for modeling correlations.

Purpose of the Study:

• To develop a method for extracting arbitrary-order interactions from complex systems.
• To leverage RBMs for efficient modeling of many-body couplings.
• To enable accurate reconstruction of higher-order structures in biological data.

Main Methods:

• Mapping Restricted Boltzmann Machines (RBMs) to generalized Potts models.
• Utilizing large-N approximations for efficient extraction of many-body couplings.
• Developing a framework for recovering higher-order interactions in generative models.

Main Results:

• Accurate recovery of two- and three-body interactions demonstrated on synthetic data.
• High-fidelity reconstruction of protein contact maps using real sequence data.
• Outperformance of state-of-the-art inverse Potts models in contact map prediction.

Conclusions:

• RBMs provide a computationally efficient and powerful tool for modeling higher-order structures.
• The developed method enables systematic extraction of complex interactions.
• This approach has significant implications for fields requiring analysis of high-dimensional categorical data.