  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 layerwise 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.
