Learning Maximum Margin Markov Networks from examples with missing labels

Structured output classifiers based on the framework of Markov Networks provide a transparent way to model statistical dependencies between output labels. The Markov Network (MN) classifier can be efficiently learned by the maximum margin method, which however requires expensive completely annotated examples. We extend the maximum margin algorithm for learning of unrestricted MN classifiers from examples with partially missing annotation of labels. The proposed algorithm translates learning into minimization of a novel loss function which is convex, has a clear connection with the supervised margin-rescaling loss, and can be efficiently optimized by first-order methods. We demonstrate the efficacy of the proposed algorithm on a challenging structured output classification problem where it beats deep neural network models trained from a much higher number of completely annotated examples, while the proposed method used only partial annotations.