Boltzmann machine learning and regularization methods for inferring evolutionary fields and couplings from a multiple sequence alignment
This work addresses protein structure and evolution analysis by improving inference methods, but it is incremental as it builds on existing Boltzmann machine learning with regularization tuning.
The study tackled the inverse Potts problem for inferring evolutionary fields and couplings from protein sequences, showing that using L2 regularization for fields and group L1 for couplings effectively recovers sparse interactions, with fields and couplings well-recovered but pairwise correlations harder to estimate for natural proteins than protein-like sequences.
The inverse Potts problem to infer a Boltzmann distribution for homologous protein sequences from their single-site and pairwise amino acid frequencies recently attracts a great deal of attention in the studies of protein structure and evolution. We study regularization and learning methods and how to tune regularization parameters to correctly infer interactions in Boltzmann machine learning. Using $L_2$ regularization for fields, group $L_1$ for couplings is shown to be very effective for sparse couplings in comparison with $L_2$ and $L_1$. Two regularization parameters are tuned to yield equal values for both the sample and ensemble averages of evolutionary energy. Both averages smoothly change and converge, but their learning profiles are very different between learning methods. The Adam method is modified to make stepsize proportional to the gradient for sparse couplings. It is shown by first inferring interactions from protein sequences and then from Monte Carlo samples that the fields and couplings can be well recovered, but that recovering the pairwise correlations in the resolution of a total energy is harder for the natural proteins than for the protein-like sequences. Selective temperature for folding/structural constrains in protein evolution is also estimated.