  Learning energy-based models (EBMs) is known to be difficult especially on
discrete data where gradient-based learning strategies cannot be applied
directly. Although ratio matching is a sound method to learn discrete EBMs, it
suffers from expensive computation and excessive memory requirements, thereby
resulting in difficulties in learning EBMs on high-dimensional data. Motivated
by these limitations, in this study, we propose ratio matching with
gradient-guided importance sampling (RMwGGIS). Particularly, we use the
gradient of the energy function w.r.t. the discrete data space to approximately
construct the provably optimal proposal distribution, which is subsequently
used by importance sampling to efficiently estimate the original ratio matching
objective. We perform experiments on density modeling over synthetic discrete
data, graph generation, and training Ising models to evaluate our proposed
method. The experimental results demonstrate that our method can significantly
alleviate the limitations of ratio matching, perform more effectively in
practice, and scale to high-dimensional problems. Our implementation is
available at https://github.com/divelab/RMwGGIS.
