The leave-one-out kernel

Recently, several attempts have been made for deriving data-dependent kernels from distribution estimates with parametric models (e.g. the Fisher kernel). In this paper, we propose a new kernel derived from any distribution estimators, parametric or nonparametric. This kernel is called the Leave-one-out kernel (i.e. LOO kernel), because the leave-one-out process plays an important role to compute this kernel. We will show that, when applied to a parametric model, the LOO kernel converges to the Fisher kernel asymptotically as the number of samples goes to infinity.