Boltzmann Machine Learning and Regularization Methods for Inferring Evolutionary Fields and Couplings From a Multiple...

Area of Science:

• Computational Biology
• Bioinformatics
• Machine Learning in Biology

Background:

• Inferring Boltzmann distributions for homologous protein sequences is crucial for understanding protein structure and evolution.
• Accurate inference requires effective methods for handling single-site and pairwise amino acid frequencies.

Purpose of the Study:

• To investigate regularization and learning methods for inferring interactions in Boltzmann machine learning.
• To tune regularization parameters for accurate inference of evolutionary interactions in protein sequences.
• To estimate selective temperatures for protein folding and structural constraints.

Main Methods:

• Employed L2 regularization for fields and group L1 for couplings, demonstrating effectiveness for sparse couplings.
• Tuned two regularization parameters to equalize sample and ensemble averages of evolutionary energy.
• Modified the Adam optimization method with gradient-proportional stepsize and soft-thresholding for group L1 regularization.

Main Results:

• Group L1 regularization proved highly effective for sparse couplings compared to L2 and L1.
• Inferred fields and couplings were well-recovered from both natural protein sequences and Monte Carlo samples.
• Recovering pairwise correlations for total energy was more challenging for natural proteins than protein-like sequences.

Conclusions:

• The developed regularization and learning strategies enable accurate inference of protein evolutionary interactions.
• The modified Adam method enhances the recovery of sparse couplings and fields.
• Understanding protein evolution benefits from accurate inference of evolutionary energy and structural constraints.