# A Tutorial on Parametric Variational Inference

arXiv: https://arxiv.org/abs/2301.01236 · HTML: https://mlsanity.com/paper/2301.01236/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 10 references that are in the map.
- First posted on arXiv 3 Jan 2023.

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

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)

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

- [On Feynman--Kac training of partial Bayesian neural networks](https://mlsanity.com/paper/2310.19608/) (2023)
- [Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models](https://mlsanity.com/paper/2308.11672/) (2023)
- [R'enyi Neural Processes](https://mlsanity.com/paper/2405.15991/) (2024)
- [A Frequentist Statistical Introduction to Variational Inference, Autoencoders, and Diffusion Models](https://mlsanity.com/paper/2510.18777/) (2025)

## Abstract (arXiv)

Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational inference is now the preferred choice for many high-dimensional models and large datasets. This tutorial introduces variational inference from the parametric perspective that dominates these recent developments, in contrast to the mean-field perspective commonly found in other introductory texts.