# Pathwise Gradient Variance Reduction with Control Variates in Variational Inference

arXiv: https://arxiv.org/abs/2410.05753 · HTML: https://mlsanity.com/paper/2410.05753/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [Yes, but Did It Work?: Evaluating Variational Inference](https://mlsanity.com/paper/1802.02538/) (2018)
- [Unbiased Implicit Variational Inference](https://mlsanity.com/paper/1808.02078/) (2018)
- [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)
- [Regularized Zero-Variance Control Variates](https://mlsanity.com/paper/1811.05073/) (2018)
- [Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization](https://mlsanity.com/paper/2006.07487/) (2020)
- [Approximation Based Variance Reduction for Reparameterization Gradients](https://mlsanity.com/paper/2007.14634/) (2020)
- [Are you using test log-likelihood correctly?](https://mlsanity.com/paper/2212.00219/) (2022)

## Abstract (arXiv)

Variational inference in Bayesian deep learning often involves computing the gradient of an expectation that lacks a closed-form solution. In these cases, pathwise and score-function gradient estimators are the most common approaches. The pathwise estimator is often favoured for its substantially lower variance compared to the score-function estimator, which typically requires variance reduction techniques. However, recent research suggests that even pathwise gradient estimators could benefit from variance reduction. In this work, we review existing control-variates-based variance reduction methods for pathwise gradient estimators to assess their effectiveness. Notably, these methods often rely on integrand approximations and are applicable only to simple variational families. To address this limitation, we propose applying zero-variance control variates to pathwise gradient estimators. This approach offers the advantage of requiring minimal assumptions about the variational distribution, other than being able to sample from it.