Selectional preference acquisition through matrix factorization with missing data

Words in an utterance are not placed in their respective slots randomly from a uniform distribution. In English, for example, a verb will rarely, if ever, follow a determiner. This is a syntactic restriction. From another perspective, one would not expect to find a word such as defenestration as the object of eat. This is what is known as the selectional preference of a word for another word in terms of its semantic domain. When this selectional preference is restricted to the arguments that a word may take on, it is called its subcategorization frame [16]. It is closely related to the problem of semantic disambiguation [24, 19, 20] whose central focus is the polysemy of words, but the definition of the problem admits more syntactic cues in that the disambiguation occurs strictly through arguments and their heads. In this paper, we lay out a novel, minimally supervised approach to inducing verb/object subcategorization frames using alternating minimization [27, 10, 4], a matrix factorization method commonly used when data is assumed to be missing. While missing data is generally not assumed in tasks dealing with semantic disambiguation or selectional preference acquisition, the pseudo-disambiguation method used to evaluate the task [18, 22, 5] is based on the assumption that there is. The pseudo-disambiguation task is a convenient but less rigorous alternative to human judgment for un-/minimally supervised approaches to inducing semantics. It is also the only such automated evaluation method for minimally supervised tasks involving semantics. While the approach at its core is based on minimizing a loss function: