# Variational Rejection Particle Filtering

arXiv: https://arxiv.org/abs/2103.15343 · HTML: https://mlsanity.com/paper/2103.15343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 29 Mar 2021.

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

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Resampled Priors for Variational Autoencoders](https://mlsanity.com/paper/1810.11428/) (2018)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [Discriminator Rejection Sampling](https://mlsanity.com/paper/1810.06758/) (2018)
- [Metropolis-Hastings Generative Adversarial Networks](https://mlsanity.com/paper/1811.11357/) (2018)
- [Approximate Inference with Amortised MCMC](https://mlsanity.com/paper/1702.08343/) (2017)
- [Regularized Autoencoders via Relaxed Injective Probability Flow](https://mlsanity.com/paper/2002.08927/) (2020)
- [Reparameterization Gradients through Acceptance-Rejection Sampling Algorithms](https://mlsanity.com/paper/1610.05683/) (2016)
- [A Contrastive Divergence for Combining Variational Inference and MCMC](https://mlsanity.com/paper/1905.04062/) (2019)
- [Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximation](https://mlsanity.com/paper/1906.10115/) (2019)
- [Variational Rejection Sampling](https://mlsanity.com/paper/1804.01712/) (2018)
- [Learning Model Reparametrizations: Implicit Variational Inference by Fitting MCMC distributions](https://mlsanity.com/paper/1708.01529/) (2017)
- [Metropolis-Hastings view on variational inference and adversarial training](https://mlsanity.com/paper/1810.07151/) (2018)
- [A Divergence Bound for Hybrids of MCMC and Variational Inference and an Application to Langevin Dynamics and SGVI](https://mlsanity.com/paper/1706.06529/) (2017)
- [Bernoulli Factories and Black-Box Reductions in Mechanism Design](https://mlsanity.com/paper/1703.04143/) (2017)
- [Bernoulli Race Particle Filters](https://mlsanity.com/paper/1903.00939/) (2019)
- [Particle filter with rejection control and unbiased estimator of the marginal likelihood](https://mlsanity.com/paper/1910.09527/) (2019)

## Abstract (arXiv)

We present a variational inference (VI) framework that unifies and leverages sequential Monte-Carlo (particle filtering) with approximate rejection sampling to construct a flexible family of variational distributions. Furthermore, we augment this approach with a resampling step via Bernoulli race, a generalization of a Bernoulli factory, to obtain a low-variance estimator of the marginal likelihood. Our framework, Variational Rejection Particle Filtering (VRPF), leads to novel variational bounds on the marginal likelihood, which can be optimized efficiently with respect to the variational parameters and generalizes several existing approaches in the VI literature. We also present theoretical properties of the variational bound and demonstrate experiments on various models of sequential data, such as the Gaussian state-space model and variational recurrent neural net (VRNN), on which VRPF outperforms various existing state-of-the-art VI methods.