In this talk, I will focus on data-driven models for semantic structure prediction following frame semantics (Fillmore, 1982), a linguistic theory that describes predicate-argument relationships and emphasizes the abstraction of predicate meaning into semantic frames. Our method exploits rich information provided by linguists in the form of a lexicon (Fillmore and Baker, 2010), as well as a small amount of annotated data, to automatically ﬁnd disambiguated semantic frames of lexical predicates present in a sentence. A frame represents semantic knowledge and requires semantic roles that are fulfilled by arguments, in the form of words and phrases within the sentence. After disambiguating each predicate to the frame it evokes, our method finds the frame’s arguments collectively via joint inference, making use of dual decomposition. Large amounts of annotated data for this task are unavailable; to this end, we model latent structure and apply semi-supervised learning, resulting in more robust models with broader coverage. Frame semantics is richer than the representation used in popular semantic role labeling systems (Kingsbury and Palmer, 2002) but less domain-specific than semantic parsers based on logical form (Ge and Mooney, 2005; Zettlemoyer and Collins, 2005); it represents a viable “middle ground” for data-driven semantic analysis of text. Compared to previous work, our method makes fewer independence assumptions and significantly outperforms past state of the art.