# Differentiable Particle Filtering via Entropy-Regularized Optimal Transport

arXiv: https://arxiv.org/abs/2102.07850 · HTML: https://mlsanity.com/paper/2102.07850/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 63 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 30 of 32)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [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)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [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)
- [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)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Massively scalable Sinkhorn distances via the Nystr"om method](https://mlsanity.com/paper/1812.05189/) (2018)
- [Particle Filter Recurrent Neural Networks](https://mlsanity.com/paper/1905.12885/) (2019)
- [Black box variational inference for state space models](https://mlsanity.com/paper/1511.07367/) (2015)
- [Discriminative Particle Filter Reinforcement Learning for Complex Partial Observations](https://mlsanity.com/paper/2002.09884/) (2020)
- [Wasserstein Discriminant Analysis](https://mlsanity.com/paper/1608.08063/) (2016)
- [An explicit analysis of the entropic penalty in linear programming](https://mlsanity.com/paper/1806.01879/) (2018)
- [How to Train Your Differentiable Filter](https://mlsanity.com/paper/2012.14313/) (2020)
- [Towards Differentiable Resampling](https://mlsanity.com/paper/2004.11938/) (2020)
- [Linear Time Sinkhorn Divergences using Positive Features](https://mlsanity.com/paper/2006.07057/) (2020)
- [Stochastic Backpropagation through Mixture Density Distributions](https://mlsanity.com/paper/1607.05690/) (2016)
- [End-To-End Semi-supervised Learning for Differentiable Particle Filters](https://mlsanity.com/paper/2011.05748/) (2020)
- [Tensor Monte Carlo: particle methods for the GPU era](https://mlsanity.com/paper/1806.08593/) (2018)

## Built on by (most cited first, 30 of 59)

- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [Differentiable SLAM-net: Learning Particle SLAM for Visual Navigation](https://mlsanity.com/paper/2105.07593/) (2021)
- [Automatic Differentiation of Programs with Discrete Randomness](https://mlsanity.com/paper/2210.08572/) (2022)
- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Online Variational Filtering and Parameter Learning](https://mlsanity.com/paper/2110.13549/) (2021)
- [Differentiable Particle Filtering without Modifying the Forward Pass](https://mlsanity.com/paper/2106.10314/) (2021)
- [Differentiable Particle Filters through Conditional Normalizing Flow](https://mlsanity.com/paper/2107.00488/) (2021)
- [Rethinking Initialization of the Sinkhorn Algorithm](https://mlsanity.com/paper/2206.07630/) (2022)
- [Reduced-Order Autodifferentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2301.11961/) (2023)
- [Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure](https://mlsanity.com/paper/2108.08129/) (2021)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters](https://mlsanity.com/paper/2111.01409/) (2021)
- [Transport with Support: Data-Conditional Diffusion Bridges](https://mlsanity.com/paper/2301.13636/) (2023)
- [Compositional Learning-based Planning for Vision POMDPs](https://mlsanity.com/paper/2112.09456/) (2021)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [Variational Marginal Particle Filters](https://mlsanity.com/paper/2109.15134/) (2021)
- [Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow](https://mlsanity.com/paper/2203.08617/) (2022)
- [Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Framework](https://mlsanity.com/paper/2307.13147/) (2023)
- [Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation](https://mlsanity.com/paper/2209.15609/) (2022)
- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)
- [On Feynman--Kac training of partial Bayesian neural networks](https://mlsanity.com/paper/2310.19608/) (2023)
- [Enhanced SMC2: Leveraging Gradient Information from Differentiable Particle Filters Within Langevin Proposals](https://mlsanity.com/paper/2407.17296/) (2024)
- [Learning to be Smooth: An End-to-End Differentiable Particle Smoother](https://mlsanity.com/paper/2502.10546/) (2025)
- [Sequential Monte Carlo for Policy Optimization in Continuous POMDPs](https://mlsanity.com/paper/2505.16732/) (2025)
- [Particle-Based Score Estimation for State Space Model Learning in Autonomous Driving](https://mlsanity.com/paper/2212.06968/) (2022)
- [De-Sequentialized Monte Carlo: a parallel-in-time particle smoother](https://mlsanity.com/paper/2202.02264/) (2022)
- [Differentiable Bootstrap Particle Filters for Regime-Switching Models](https://mlsanity.com/paper/2302.10319/) (2023)
- [Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers](https://mlsanity.com/paper/2304.14390/) (2023)
- [Learning Differentiable Particle Filter on the Fly](https://mlsanity.com/paper/2312.05955/) (2023)

## Abstract (arXiv)

Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.