Latent Template Induction with Gumbel-CRFs Appendix

As noted in the main paper, the baseline estimator PM-MRF also involve in-depth exploitation of the structure of models and gradients, thus being quite competitive. Here we give a detailed discussion. Papandreou and Yuille [4] proposed the Perturb-and-MAP Random Field, an efficient sampling method for general Markov Random Field. This MAP ẑ from the perturbed Φ can be viewed as a biased sample from the original MRF. This method is much faster than the MCMC sampler when an efficient MAP algorithm exists.