# Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling

arXiv: https://arxiv.org/abs/2002.05616 · HTML: https://mlsanity.com/paper/2002.05616/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2020.

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

- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Learning Iterative Reasoning through Energy Diffusion](https://mlsanity.com/paper/2406.11179/) (2024)
- [Learning Iterative Reasoning through Energy Minimization](https://mlsanity.com/paper/2206.15448/) (2022)
- [Active Slices for Sliced Stein Discrepancy](https://mlsanity.com/paper/2102.03159/) (2021)
- [Adversarial Stein Training for Graph Energy Models](https://mlsanity.com/paper/2108.12982/) (2021)

## Abstract (arXiv)

We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) defined by a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize the discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing q(x) to minimize this discrepancy produces a novel method for training unnormalized models which scales more gracefully than existing methods. The ability to both learn and compare models is a unique feature of the proposed method.