Implicit Differentiation by Perturbation

This paper proposes a simple and efficient finite difference method for implicit differentiationof marginal inference results in discrete graphical models. Given an arbitrary loss function, defined on marginals, we show that the derivatives of this loss with respect to model parameters can be obtained by running the inference procedure twice, on slightly perturbed model parameters. Thismethod can be used with approximate inference, with a loss function over approximate marginals. Convenient choices of loss functions makeit practical to fit graphical models with hidden variables, high treewidth and/or model misspecification.