# Variational Prediction

arXiv: https://arxiv.org/abs/2307.07568 · HTML: https://mlsanity.com/paper/2307.07568/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 14 references that are in the map.
- First posted on arXiv 14 Jul 2023.

## Builds on (most cited first, 5 of 5)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)
- [Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference](https://mlsanity.com/paper/1703.09194/) (2017)
- [Bayesian Dark Knowledge](https://mlsanity.com/paper/1506.04416/) (2015)

## Built on by (most cited first, 2 of 2)

- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [A Critical Synthesis of Uncertainty Quantification and Foundation Models in Monocular Depth Estimation](https://mlsanity.com/paper/2501.08188/) (2025)

## Abstract (arXiv)

Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In this paper, we present variational prediction, a technique for directly learning a variational approximation to the posterior predictive distribution using a variational bound. This approach can provide good predictive distributions without test time marginalization costs. We demonstrate Variational Prediction on an illustrative toy example.