Structure Learning Constrained by Node-Specific Degree Distribution

Abstract

We consider the problem of learning the structure of a Markov Random Field (MRF) when the node-specific degree distribution is provided. The problem setting is inspired by protein contact map prediction in which residue-specific contact number distribution can be estimated without predicting individual contacts beforehand. We replace the widely used l_1 regularization with a node-specific regularization derived from the predicted degree distribution and optimize the objective function using an Iterative Maximum Cost Bipartite Matching algorithm. When a node is predicted to have k edges, its largest k regularization coefficients are reduced, promoting appearance of k edges for that node. We predict node-specific degree distribution using multiple 2nd-order Conditional Neural Fields integrating both local and global information of a protein. Experimental results show that for protein contact prediction our approach yields a significant accuracy improvement when the predicted contact number is reasonably good.