Learning state machine-based string edit kernels

During the past few years, several works have been done to derive string kernels from probability distributions. For instance, the Fisher kernel uses a generative model M (e.g. a hidden markov model) and compares two strings according to how they are generated by M . On the other hand, the marginalized kernels allow the computation of the joint similarity between two instances by summing conditional probabilities. In this paper, we adapt this approach to edit distance-based conditional distributions and we present a way to learn a new string edit kernel. We show that the practical computation of such a kernel between two strings x and x built from an alphabet Σ requires (i) to learn edit probabilities in the form of the parameters of a stochastic state machine and (ii) to calculate an infinite sum over Σ by resorting to the intersection of probabilistic automata as done for rational kernels. We show on a handwritten character recognition task that our new kernel outperforms not only the state of the art string kernels and string edit kernels but also the standard edit distance used by a neighborhood-based classifier.