Prediction approach for ising model estimation

We consider the graph estimation for Ising model from observed binary data. Popular approaches in the literature are largely penalized sparse selection procedures that depend on tuning parameters to be selected. The output of such procedures is usually one single sparse graph without any ranking information of the individual edges. In scientific practice, however, it is more desirable to be able to rank all potential edges based on their statistical significance, and select the sparse graph by thresholding. In this paper, we propose a novel PRediction Approach for Ising Model Estimation (PRAIME). The proposed framework reformulates Ising model estimation as the prediction of the observed data, and provides an estimate and a statistical significance measure of the Ising model parameter for each node pair using only the predicted values. Thus it enables the ranking all potential edges and the flexible sparse graph selection by thresholding, and allows the researchers to use the predictive algorithm of their choice. We implemented PRAIME using random forest, illustrated the advantage of PRAIME over the penalized sparse selection approaches in accuracy and flexibility using synthetic data, and applied it to a congress co-sponsorship dataset.