Stochastic Contextual Edit Distance and Probabilistic FSTs

String similarity is most often measured by weighted or unweighted edit distance d(x, y). Ristad and Yianilos (1998) de-fined stochastic edit distance—a probabil-ity distribution p(y | x) whose parame-ters can be trained from data. We general-ize this so that the probability of choosing each edit operation can depend on contex-tual features. We show how to construct and train a probabilistic finite-state trans-ducer that computes our stochastic con-textual edit distance. To illustrate the im-provement from conditioning on context, we model typos found in social media text.