A Logic-based Approach to Generatively Defined Discriminative Modeling

Abstract: Conditional random fields (CRFs) are usually specified by graphical models but in this paper we propose to use probabilistic logic programs and specify them generatively. Our intension is first to provide a unified approach to CRFs for complex modeling through the use of a Turing complete language and second to offer a convenient way of realizing generative-discriminative pairs in machine learning to compare generative and discriminative models and choose the best model. We implemented our approach as the D-PRISM language by modifying PRISM, a logic-based probabilistic modeling language for generative modeling, while exploiting its dynamic programming mechanism for efficient probability computation. We tested D-PRISM with logistic regression, a linear-chain CRF and a CRF-CFG and empirically confirmed their excellent discriminative performance compared to their generative counterparts, i.e.\ naive Bayes, an HMM and a PCFG. We also introduced new CRF models, CRF-BNCs and CRF-LCGs. They are CRF versions of Bayesian network classifiers and probabilistic left-corner grammars respectively and easily implementable in D-PRISM. We empirically showed that they outperform their generative counterparts as expected.