# Variational Marginal Particle Filters

arXiv: https://arxiv.org/abs/2109.15134 · HTML: https://mlsanity.com/paper/2109.15134/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 56 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [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)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (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)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [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)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [Tighter Variational Bounds are Not Necessarily Better](https://mlsanity.com/paper/1802.04537/) (2018)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Particle Filter Networks with Application to Visual Localization](https://mlsanity.com/paper/1805.08975/) (2018)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [An Introduction to Probabilistic Programming](https://mlsanity.com/paper/1809.10756/) (2018)
- [Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors](https://mlsanity.com/paper/1805.11122/) (2018)
- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [Hamiltonian Variational Auto-Encoder](https://mlsanity.com/paper/1805.11328/) (2018)
- [Variational Boosting: Iteratively Refining Posterior Approximations](https://mlsanity.com/paper/1611.06585/) (2016)
- [Particle Filter Recurrent Neural Networks](https://mlsanity.com/paper/1905.12885/) (2019)
- [The Variational Gaussian Process](https://mlsanity.com/paper/1511.06499/) (2015)
- [Discriminative Particle Filter Reinforcement Learning for Complex Partial Observations](https://mlsanity.com/paper/2002.09884/) (2020)
- [Nested Sequential Monte Carlo Methods](https://mlsanity.com/paper/1502.02536/) (2015)
- [Towards Differentiable Resampling](https://mlsanity.com/paper/2004.11938/) (2020)
- [Stochastic Backpropagation through Mixture Density Distributions](https://mlsanity.com/paper/1607.05690/) (2016)

## Built on by (most cited first, 6 of 6)

- [Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Framework](https://mlsanity.com/paper/2307.13147/) (2023)
- [Particle-Based Score Estimation for State Space Model Learning in Autonomous Driving](https://mlsanity.com/paper/2212.06968/) (2022)
- [Differentiable and Stable Long-Range Tracking of Multiple Posterior Modes](https://mlsanity.com/paper/2404.08789/) (2024)
- [Diffusion differentiable resampling](https://mlsanity.com/paper/2512.10401/) (2025)
- [Massively Parallel Reweighted Wake-Sleep](https://mlsanity.com/paper/2305.11022/) (2023)
- [Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs](https://mlsanity.com/paper/2412.03271/) (2024)

## Abstract (arXiv)

Variational inference for state space models (SSMs) is known to be hard in general. Recent works focus on deriving variational objectives for SSMs from unbiased sequential Monte Carlo estimators. We reveal that the marginal particle filter is obtained from sequential Monte Carlo by applying Rao-Blackwellization operations, which sacrifices the trajectory information for reduced variance and differentiability. We propose the variational marginal particle filter (VMPF), which is a differentiable and reparameterizable variational filtering objective for SSMs based on an unbiased estimator. We find that VMPF with biased gradients gives tighter bounds than previous objectives, and the unbiased reparameterization gradients are sometimes beneficial.