Gradient-Guided Importance Sampling for Learning Discrete Energy-Based Models

Meng Liu, Haoran Liu, Shuiwang Ji

Keywords: Discrete energy-based models, ratio matching, importance sampling, gradient

Abstract: 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 requirement, thereby resulting in difficulties for learning EBMs on high-dimensional data. In this study, we propose ratio matching with gradient-guided importance sampling (RMwGGIS) to alleviate the above limitations. Particularly, we leverage the gradient of the energy function w.r.t. the discrete data space to approximately construct the provable 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 and graph generation to evaluate our proposed method. The experimental results demonstrate that our method can significantly alleviate the limitations of ratio matching and perform more effectively in practice.