  Unsupervised ensemble learning has long been an interesting yet challenging
problem that comes to prominence in recent years with the increasing demand of
crowdsourcing in various applications. In this paper, we propose a novel
method-- unsupervised ensemble learning via Ising model approximation (unElisa)
that combines a pruning step with a predicting step. We focus on the binary
case and use an Ising model to characterize interactions between the ensemble
and the underlying true classifier. The presence of an edge between an observed
classifier and the true classifier indicates a direct dependence whereas the
absence indicates the corresponding one provides no additional information and
shall be eliminated. This observation leads to the pruning step where the key
is to recover the neighborhood of the true classifier. We show that it can be
recovered successfully with exponentially decaying error in the
high-dimensional setting by performing nodewise $\ell_1$-regularized logistic
regression. The pruned ensemble allows us to get a consistent estimate of the
Bayes classifier for predicting. We also propose an augmented version of
majority voting by reversing all labels given by a subgroup of the pruned
ensemble. We demonstrate the efficacy of our method through extensive numerical
experiments and through the application to EHR-based phenotyping prediction on
Rheumatoid Arthritis (RA) using data from Partners Healthcare System.
