Maximum Entropy Discrimination Markov Networks
Jun Zhu, Eric P. Xing · 2009
Standard max-margin structured prediction methods concentrate directly on the inputoutput mapping, and the lack of an elegant probabilistic interpretation causes limitations. In this paper, we present a novel framework called Maximum Entropy Discrimination Markov Networks (MaxEntNet) to do Bayesian max-margin structured learning by using expected margin constraints to define a feasible distribution subspace and applying the maximum entropy principle to choose the best distribution from this subspace. We show that MaxEntNet subsumes the standard max-margin Markov networks (M 3 N) as a spacial case where the predictive model is assumed to be linear and the parameter prior is a standard normal. Based on this understanding, we propose the Laplace max-margin Markov networks (LapM 3 N) which use the Laplace prior instead of the standard normal. We show that the adoption of a Laplace prior of the parameter makes LapM 3 N enjoy properties expected from a sparsified M 3 N. Unlike the L1-regularized maximum likelihood estimation which sets small weights to zeros to achieve sparsity, LapM 3 N posteriorly weights the parameters and features with smaller weights are shrunk more. This posterior weighting effect makes LapM 3 N more stable with respect to the magnitudes of the regularization coefficients and more generalizable. To