Learning to model spatial dependency: Semi-supervised discriminative random fields

We present a new, semi-supervised extension of discriminative random fields (DRFs) that efficiently exploits labeled and unlabeled training data to achieve improved accuracy in a variety of image processing tasks. We formulate DRF training as a form of MAP estimation that combines conditional loglikelihood on labeled data, given a data-dependent prior, with a conditional entropy regularizer defined on unlabeled data. Although the training objective is no longer concave, we develop an efficient local optimization procedure that improves standard supervised DRF training. We then apply semi-supervised DRFs to a set of image segmentation problems on synthetic and real data sets, and achieve significant improvements over supervised DRFs in each case.