# Gradient-Guided Importance Sampling for Learning Binary Energy-Based Models

arXiv: https://arxiv.org/abs/2210.05782 · HTML: https://mlsanity.com/paper/2210.05782/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 70 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Training Region-based Object Detectors with Online Hard Example Mining](https://mlsanity.com/paper/1604.03540/) (2016)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition](https://mlsanity.com/paper/1503.02101/) (2015)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [Searching for Activation Functions](https://mlsanity.com/paper/1710.05941/) (2017)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [Residual Energy-Based Models for Text Generation](https://mlsanity.com/paper/2004.11714/) (2020)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [Flow Contrastive Estimation of Energy-Based Models](https://mlsanity.com/paper/1912.00589/) (2019)
- [Learning Descriptor Networks for 3D Shape Synthesis and Analysis](https://mlsanity.com/paper/1804.00586/) (2018)
- [Learning Energy-Based Models as Generative ConvNets via Multi-grid Modeling and Sampling](https://mlsanity.com/paper/1709.08868/) (2017)
- [Learning Discrete Energy-based Models via Auxiliary-variable Local Exploration](https://mlsanity.com/paper/2011.05363/) (2020)
- [Conditional Noise-Contrastive Estimation of Unnormalised Models](https://mlsanity.com/paper/1806.03664/) (2018)
- [Adversarial Contrastive Estimation](https://mlsanity.com/paper/1805.03642/) (2018)
- [Energy-based models for atomic-resolution protein conformations](https://mlsanity.com/paper/2004.13167/) (2020)
- [Gradient Importance Sampling](https://mlsanity.com/paper/1507.05781/) (2015)

## Built on by (most cited first, 6 of 6)

- [Concrete Score Matching: Generalized Score Matching for Discrete Data](https://mlsanity.com/paper/2211.00802/) (2022)
- [Learning Unnormalized Statistical Models via Compositional Optimization](https://mlsanity.com/paper/2306.07485/) (2023)
- [Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces](https://mlsanity.com/paper/2412.01019/) (2024)
- [A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence](https://mlsanity.com/paper/2408.01022/) (2024)
- [Fine-Tuning Low-Bit Models with Gradient in Quantized Code Space](https://mlsanity.com/paper/2608.30908/) (2026)
- [Training Discrete Energy-Based Models with Energy Discrepancy](https://mlsanity.com/paper/2307.07595/) (2023)

## Abstract (arXiv)

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.