On some properties of the low-dimensional Gumbel perturbations in the Perturb-and-MAP model.

The full-order Perturb-and-MAP model is equivalent to the Gibbs distribution, but its applicability is limited. Empirically it is shown that low-dimensional Gumbel perturbations allow to approximate the Gibbs distribution but their theoretical properties remain unclear. In this note we fill this gap. [ABSTRACT FROM AUTHOR]