Structure Learning Constrained by Node-Specific Degree Distribution

We consider the problem of learning the structure of a Markov Random Field (MRF) when a node-specific degree distribution is provided. The problem setting is inspired by protein contact map (i.e., graph) prediction in which the contact number (i.e., degree) of an individual residue (i.e., node) can be predicted without knowing the contact graph. We formulate this problem using maximum pseudo-likelihood plus a node-specific l1 regularization derived from the predicted degree distribution. Intuitively, when a node have k predicted edges, we dynamically reduce the regularization coefficients of the k most possible edges to promote their occurrence. We then optimize the objective function using ADMM and an Iterative Maximum Cost Bipartite Matching algorithm. Our experimental results show that using degree distribution as a constraint may lead to significant performance gain when the predicted degree has good accuracy.