This paper presents an approach to partial parsing of natural language sentences that makes global inference on top of the outcome of hierarchically learned local classifiers. The best decomposition of a sentence into clauses is chosen using a dynamic programming based scheme that takes into account previously identified partial solutions. This inference scheme applies learning at several levels—when identifying potential clauses and when scoring partial solutions. The classifiers are trained in a hierarchical fashion, building on previous classifications. The method presented significantly outperforms the best methods known so far for clause identification.