The inverse Potts problem to infer the Boltzmann distribution for homologous protein sequences from their single-site and pairwise  frequencies recently attracts a great deal of attention due to its capacity to accurately predict residue-residue contacts in a 3D protein complex. A Boltzmann machine for the accurate estimation of the field and coupling interactions, which is required for other studies in protein evolution and folding, is studied about learning methods , regularization models and a tuning method of regularization parameters in order to infer the interactions with reasonable characteristics . Using L_2 regularization for fields, group L_1 for couplings is shown to be very effective for parse couplings in comparison with L_2 and with L_1. Two regularization parameters for fields and couplings are tuned to yield equal values for both the sample average and the ensemble average of evolutionary energies of natural proteins. Both the averages along a learning process smoothly change and converge, but their  profiles are very different between the learning methods. Most per-parameter adaptive learning methods invented for machine learning cannot learn reasonable parameters for sparse-interaction systems. A modified Adam (ModAdam) method is invented to make step-size proportional to the partial derivative for sparse couplings and to use a soft thresholding function for group L_1. 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 by the group L_1 and the ModAdam method. However, the distribution of evolutionary energies over natural proteins is shifted towards lower energies from that of Monte Carlo samples, indicating that there may be higher-order interactions to favor natural 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 and to use a soft-thresholding function for group L_1. 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 .
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the
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amino acid
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due to its capacity to accurately predict residue-residue contacts in a 3D protein complex. A Boltzmann machine for the accurate estimation of the field and coupling interactions, which is required for other studies in protein evolution
in the studies of protein structure and evolution. We study regularization and learning methods
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folding, is studied about learning methods , regularization models and a tuning method of regularization parameters in order to infer the interactions with reasonable characteristics
how to tune regularization parameters to correctly infer interactions in Boltzmann machine learning
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parse
sparse
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with
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for fields and couplings
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average and the ensemble average of evolutionary energies of natural proteins. Both the averages along a learning process
and ensemble averages of evolutionary energy. Both averages
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learning
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the
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Most per-parameter adaptive learning methods invented for machine learning cannot learn reasonable parameters for sparse-interaction systems. A modified Adam (ModAdam) method is invented to make step-size
The Adam method is modified to make stepsize
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partial derivative
gradient
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soft thresholding
soft-thresholding
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by the group L_1 and the ModAdam method. However, the distribution of evolutionary energies over natural proteins is shifted towards lower energies from that of Monte Carlo samples, indicating that there may be higher-order interactions to favor natural sequences
, 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