# The Variational Predictive Natural Gradient

arXiv: https://arxiv.org/abs/1903.02984 · HTML: https://mlsanity.com/paper/1903.02984/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2019.

## Built on by (most cited first, 4 of 4)

- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [Automated Efficient Estimation using Monte Carlo Efficient Influence Functions](https://mlsanity.com/paper/2403.00158/) (2024)
- [Optimization Guarantees for Square-Root Natural-Gradient Variational Inference](https://mlsanity.com/paper/2507.07853/) (2025)
- [Natural Gradient VI: Guarantees for Non-Conjugate Models](https://mlsanity.com/paper/2510.19163/) (2025)

## Abstract (arXiv)

Variational inference transforms posterior inference into parametric optimization thereby enabling the use of latent variable models where otherwise impractical. However, variational inference can be finicky when different variational parameters control variables that are strongly correlated under the model. Traditional natural gradients based on the variational approximation fail to correct for correlations when the approximation is not the true posterior. To address this, we construct a new natural gradient called the Variational Predictive Natural Gradient (VPNG). Unlike traditional natural gradients for variational inference, this natural gradient accounts for the relationship between model parameters and variational parameters. We demonstrate the insight with a simple example as well as the empirical value on a classification task, a deep generative model of images, and probabilistic matrix factorization for recommendation.