Computing the Expected Edit Distance from a String to a PFA

Abstract

Abstract. In a number of fields one is to compare a witness string with a distribution. One possibility is to compute the probability of the string for that distribution. Another, giving a more global view, is to compute the expected edit distance from a string randomly drawn to the witness string. This number is often used to measure the performance of a prediction, the goal then being to return the median string, or the string with smallest expected distance. To be able to measure this, computing the distance between a hypothesis and that distribution is necessary. This paper proposes two solutions for computing this value, when the distribution is defined with a probabilistic finite state automaton. The first is exact but has a cost which can be exponential in the length of the input string, whereas the second is a Fpras.

Computing the Expected Edit Distance from a String to a Probabilistic Finite-State Automaton

“…In the conference version of this paper [6] we presented two results. The first is that the expected edit distance is computable, and that when the weights of the Pfa are rational, then the result itself is rational as well.…”