Maximum Entropy Discrimination Markov Networks

Jun Zhu; Eric P. Xing

The standard maximum margin approach for structured prediction lacks a straightforward probabilistic interpretation of the learning scheme and the prediction rule. Therefore its unique advantages such as dual sparseness and kernel tricks cannot be easily conjoined with the merits of a probabilistic model such as Bayesian regularization, model averaging, and ability to model hidden variables. In this paper, we present a new general framework called maximum entropy discrimination Markov networks (MaxEnDNet, or simply, MEDN), which integrates these two approaches and combines and extends their merits. Major innovations of this approach include: 1) It extends the conventional max-entropy discrimination learning of classification rules to a new structural max-entropy discrimination paradigm of learning a distribution of Markov networks. 2) It generalizes the extant Markov network structured-prediction rule based on a point estimator of model coefficients to an averaging model akin to a Bayesian predictor that integrates over a learned posterior distribution of model coefficients. 3) It admits flexible entropic regularization of the model during learning. By plugging in different prior distributions of the model coefficients, it subsumes the well-known maximum margin Markov networks (M³N) as a special case, and leads to a model similar to an L₁-regularized M³N that is simultaneously primal and dual sparse, or other new types of Markov networks. 4) It applies a modular learning algorithm that combines existing variational inference techniques and convex-optimization based M³N solvers as subroutines. Essentially, MEDN can be understood as a jointly maximum likelihood and maximum margin estimate of Markov network. It represents the first successful attempt to combine maximum entropy learning (a dual form of maximum likelihood learning) with maximum margin learning of Markov network for structured input/output problems; and the basic principle can be generalized to learning arbitrary graphical models, such as the generative Bayesian networks or models with structured hidden variables. We discuss a number of theoretical properties of this approach, and show that empirically it outperforms a wide array of competing methods for structured input/output learning on both synthetic and real OCR and web data extraction data sets.

Maximum Entropy Discrimination Markov Networks

Abstract