... on, onto,outside, over, through, to, toward, towards, under,underneath, until, up, upon, with, within, without),which we adopt from previous work. Every prepo-sitional phrase (PP) that is governed ... prepositions.4 Linear Classifiers for GrammaticalError CorrectionIn this section, we formulate GEC as a classificationproblem and describe the feature sets for each task.4.1 Linear ClassifiersWe ... multi-class classifica-tion problem with m classes can be cast as m binaryclassification problems in a one-vs-rest arrangement.The prediction of the classifier is the class with thehighest scoreˆY...