Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: For Markov chain Monte Carlo methods, one of the greatest discrepancies between theory and system is the scan order — while most theoretical development on the mixing time analysis deals with random updates, real-world systems are implemented with systematic scans. We bridge this gap for models that exhibit a bipartite structure, including, most notably, the Restricted/Deep Boltzmann Machine. The de facto implementation for these models scans variables in a layer-wise fashion. We show that the Gibbs sampler with a layerwise alternating scan order has its relaxation time (in terms of epochs) no larger than that of a random-update Gibbs sampler (in terms of variable updates). We also construct examples to show that this bound is asymptotically tight. Through standard inequalities, our result also implies a comparison on the mixing times.

LAYERWISE SYSTEMATIC SCAN: DEEP BOLTZMANN MACHINES AND BEYOND