# Generative Particle Variational Inference via Estimation of Functional Gradients

arXiv: https://arxiv.org/abs/2103.01291 · HTML: https://mlsanity.com/paper/2103.01291/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Structured and Efficient Variational Deep Learning with Matrix Gaussian Posteriors](https://mlsanity.com/paper/1603.04733/) (2016)
- [Bayesian Hypernetworks](https://mlsanity.com/paper/1710.04759/) (2017)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [Bayesian Dark Knowledge](https://mlsanity.com/paper/1506.04416/) (2015)
- [Implicit Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1711.01297/) (2017)
- [Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learning](https://mlsanity.com/paper/1611.01722/) (2016)
- [Variational Inference for Gaussian Process Models with Linear Complexity](https://mlsanity.com/paper/1711.10127/) (2017)
- [Stein Neural Sampler](https://mlsanity.com/paper/1810.03545/) (2018)
- [An introduction to sampling via measure transport](https://mlsanity.com/paper/1602.05023/) (2016)
- [Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families](https://mlsanity.com/paper/1506.02564/) (2015)

## Abstract (arXiv)

Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions.