# Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow

arXiv: https://arxiv.org/abs/2203.08617 · HTML: https://mlsanity.com/paper/2203.08617/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 16 Mar 2022.

## Builds on (most cited first, 18 of 18)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Noise Flow: Noise Modeling with Conditional Normalizing Flows](https://mlsanity.com/paper/1908.08453/) (2019)
- [Particle Filter Networks with Application to Visual Localization](https://mlsanity.com/paper/1805.08975/) (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)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Backprop KF: Learning Discriminative Deterministic State Estimators](https://mlsanity.com/paper/1605.07148/) (2016)
- [Structured Output Learning with Conditional Generative Flows](https://mlsanity.com/paper/1905.13288/) (2019)
- [Gaussian Process Conditional Density Estimation](https://mlsanity.com/paper/1810.12750/) (2018)
- [How to Train Your Differentiable Filter](https://mlsanity.com/paper/2012.14313/) (2020)
- [The Kernel Mixture Network: A Nonparametric Method for Conditional Density Estimation of Continuous Random Variables](https://mlsanity.com/paper/1705.07111/) (2017)
- [Differentiable Particle Filters through Conditional Normalizing Flow](https://mlsanity.com/paper/2107.00488/) (2021)
- [End-To-End Semi-supervised Learning for Differentiable Particle Filters](https://mlsanity.com/paper/2011.05748/) (2020)
- [Bottleneck Conditional Density Estimation](https://mlsanity.com/paper/1611.08568/) (2016)

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

- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Differentiable Bootstrap Particle Filters for Regime-Switching Models](https://mlsanity.com/paper/2302.10319/) (2023)
- [Learning Differentiable Particle Filter on the Fly](https://mlsanity.com/paper/2312.05955/) (2023)
- [Revisiting semi-supervised training objectives for differentiable particle filters](https://mlsanity.com/paper/2405.01251/) (2024)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)

## Abstract (arXiv)

Tuning of measurement models is challenging in real-world applications of sequential Monte Carlo methods. Recent advances in differentiable particle filters have led to various efforts to learn measurement models through neural networks. But existing approaches in the differentiable particle filter framework do not admit valid probability densities in constructing measurement models, leading to incorrect quantification of the measurement uncertainty given state information. We propose to learn expressive and valid probability densities in measurement models through conditional normalizing flows, to capture the complex likelihood of measurements given states. We show that the proposed approach leads to improved estimation performance and faster training convergence in a visual tracking experiment.