In this paper, we present a novel and general framework called Maximum Entropy Discrimination Markov Networks (MaxEnDNet), which integrates the max-margin structured learning and Bayesian-style estimation and combines and extends their merits. Major innovations of this model include: 1) It generalizes the extant Markov network prediction rule based on a point estimator of weights to a Bayesian-style estimator that integrates over a learned distribution of the weights. 2) It extends the conventional max-entropy discrimination learning of classification rule to a new structural max-entropy discrimination paradigm of learning the distribution of Markov networks. 3) It subsumes the well-known and powerful Maximum Margin Markov network (M @math N) as a special case, and leads to a model similar to an @math -regularized M @math N that is simultaneously primal and dual sparse, or other types of Markov network by plugging in different prior distributions of the weights. 4) It offers a simple inference algorithm that combines existing variational inference and convex-optimization based M @math N solvers as subroutines. 5) It offers a PAC-Bayesian style generalization bound. This work represents the first successful attempt to combine Bayesian-style learning (based on generative models) with structured maximum margin learning (based on a discriminative model), and outperforms a wide array of competing methods for structured input output learning on both synthetic and real data sets.
Although the parameter distribution @math in Theorem has a similar form as that of the Bayesian Conditional Random Fields (BCRFs) , MaxEnDNet is fundamentally different from BCRFs as we have stated. @cite_2 present an interesting confidence-weighted linear classification method, which automatically estimates the mean and variance of model parameters in online learning. The procedure is similar to (but indeed different from) our variational Bayesian method of Laplace MaxEnDNet.
@cite_2
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This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classification tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the 'relevance vector machine' (RVM), a model of identical functional form to the popular and state-of-the-art 'support vector machine' (SVM). We demonstrate that by exploiting a probabilistic Bayesian learning framework, we can derive accurate prediction models which typically utilise dramatically fewer basis functions than a comparable SVM while offering a number of additional advantages. These include the benefits of probabilistic predictions, automatic estimation of 'nuisance' parameters, and the facility to utilise arbitrary basis functions (e.g. non-'Mercer' kernels). We detail the Bayesian framework and associated learning algorithm for the RVM, and give some illustrative examples of its application along with some comparative benchmarks. We offer some explanation for the exceptional degree of sparsity obtained, and discuss and demonstrate some of the advantageous features, and potential extensions, of Bayesian relevance learning.