Learning Structured Outputs via Kernel Dependency Estimation and Stochastic Grammars

We focus on graph-valued outputs in supervised learning and propose a novel solution to the pre-image problem in the kernel dependency estimation framework. Output structures are generated by a stochastic grammar and the output feature space is directly associated with the set of productions for the grammar. The regression estimation step learns to map input examples into a feature vector that counts the number of applications of each production rule. A max-propagation algorithm finally builds the predicted output according to the normalized counts. We test our method on a ambiguous context free grammar (CFG) parse tree reconstruction problem. We show on an artificial dataset that mimics the prepositional attachment problem how learning the number of applications of each production rule on a per example base allows CFG parser to better tackle ambiguity issues.