# Joint control variate for faster black-box variational inference

arXiv: https://arxiv.org/abs/2210.07290 · HTML: https://mlsanity.com/paper/2210.07290/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 20 of 20)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [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)
- [REBAR: Low-variance, unbiased gradient estimates for discrete latent variable models](https://mlsanity.com/paper/1703.07370/) (2017)
- [Variance-Reduced Methods for Machine Learning](https://mlsanity.com/paper/2010.00892/) (2020)
- [Variance reduction properties of the reparameterization trick](https://mlsanity.com/paper/1809.10330/) (2018)
- [Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning](https://mlsanity.com/paper/1402.4419/) (2014)
- [Reducing Reparameterization Gradient Variance](https://mlsanity.com/paper/1705.07880/) (2017)
- [Using Large Ensembles of Control Variates for Variational Inference](https://mlsanity.com/paper/1810.12482/) (2018)
- [Finito: A Faster, Permutable Incremental Gradient Method for Big Data Problems](https://mlsanity.com/paper/1407.2710/) (2014)
- [Approximation Based Variance Reduction for Reparameterization Gradients](https://mlsanity.com/paper/2007.14634/) (2020)
- [Stochastic Optimization with Variance Reduction for Infinite Datasets with Finite-Sum Structure](https://mlsanity.com/paper/1610.00970/) (2016)
- [Amortized variance reduction for doubly stochastic objectives](https://mlsanity.com/paper/2003.04125/) (2020)
- [Lightweight Stochastic Optimization for Minimizing Finite Sums with Infinite Data](https://mlsanity.com/paper/1806.02927/) (2018)

## Abstract (arXiv)

Black-box variational inference performance is sometimes hindered by the use of gradient estimators with high variance. This variance comes from two sources of randomness: Data subsampling and Monte Carlo sampling. While existing control variates only address Monte Carlo noise, and incremental gradient methods typically only address data subsampling, we propose a new "joint" control variate that jointly reduces variance from both sources of noise. This significantly reduces gradient variance, leading to faster optimization in several applications.