  Restricted Boltzmann Machine (RBM) is a bipartite graphical model that is
used as the building block in energy-based deep generative models. Due to
numerical stability and quantifiability of the likelihood, RBM is commonly used
with Bernoulli units. Here, we consider an alternative member of exponential
family RBM with leaky rectified linear units -- called leaky RBM. We first
study the joint and marginal distributions of leaky RBM under different
leakiness, which provides us important insights by connecting the leaky RBM
model and truncated Gaussian distributions. The connection leads us to a simple
yet efficient method for sampling from this model, where the basic idea is to
anneal the leakiness rather than the energy; -- i.e., start from a fully
Gaussian/Linear unit and gradually decrease the leakiness over iterations. This
serves as an alternative to the annealing of the temperature parameter and
enables numerical estimation of the likelihood that are more efficient and more
accurate than the commonly used annealed importance sampling (AIS). We further
demonstrate that the proposed sampling algorithm enjoys faster mixing property
than contrastive divergence algorithm, which benefits the training without any
additional computational cost.
