mlsanityData to 7 Oct 2026

Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters

arXiv 2111.01409 ↗First posted 2 Nov 2021stat.ML cs.LGcited by 9

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Abstract (arXiv)

It has been widely documented that the sampling and resampling steps in particle filters cannot be differentiated. The itshape reparameterisation trick was introduced to allow the sampling step to be reformulated into a differentiable function. We extend the itshape reparameterisation trick to include the stochastic input to resampling therefore limiting the discontinuities in the gradient calculation after this step. Knowing the gradients of the prior and likelihood allows us to run particle Markov Chain Monte Carlo (p-MCMC) and use the No-U-Turn Sampler (NUTS) as the proposal when estimating parameters. We compare the Metropolis-adjusted Langevin algorithm (MALA), Hamiltonian Monte Carlo with different number of steps and NUTS. We consider two state-space models and show that NUTS improves the mixing of the Markov chain and can produce more accurate results in less computational time.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 20 of its 58 references that are in the map. First posted on arXiv 2 Nov 2021.

Builds on

20 of 58 references.

References · 20

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2013Auto-Encoding Variational Bayescited by 3,980
  3. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,708
  4. 2017A Conceptual Introduction to Hamiltonian Monte Carlocited by 207
  5. 2018Particle Filter Networks with Application to Visual Localizationcited by 64
  6. 2021Differentiable Particle Filtering via Entropy-Regularized Optimal Transportcited by 59
  7. 2018Differentiable Particle Filters: End-to-End Learning with Algorithmic Priorscited by 58
  8. 2019Particle Filter Recurrent Neural Networkscited by 36
  9. 2017Geometric integrators and the Hamiltonian Monte Carlo methodcited by 25
  10. 2020How to Train Your Differentiable Filtercited by 23
  11. 2020Towards Differentiable Resamplingcited by 19
  12. 2021Differentiable Particle Filtering without Modifying the Forward Passcited by 18
8 more
  1. 2021Differentiable Particle Filters through Conditional Normalizing Flowcited by 15
  2. 2020End-To-End Semi-supervised Learning for Differentiable Particle Filterscited by 12
  3. 2015Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Modelscited by 6
  4. 2019Stochastic quasi-Newton with line-search regularizationcited by 6
  5. 2013Particle Metropolis-Hastings using gradient and Hessian informationcited by 4
  6. 2016Identifying the Optimal Integration Time in Hamiltonian Monte Carlocited by 4
  7. 2013Particle approximations of the score and observed information matrix for parameter estimation in state space models with linear computational costcited by 2
  8. 2014Particle Metropolis adjusted Langevin algorithms for state space modelscited by 2

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Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 3; 2025: 3.

9 papers.

  1. 2022Automatic Differentiation of Programs with Discrete Randomnesscited by 28
  2. 2023An overview of differentiable particle filters for data-adaptive sequential Bayesian inferencecited by 23
  3. 2024Normalizing Flow-based Differentiable Particle Filterscited by 10
  4. 2023Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inferencecited by 5
  5. 2024Enhanced SMC2: Leveraging Gradient Information from Differentiable Particle Filters Within Langevin Proposalscited by 4
  6. 2025DiffPF: Differentiable Particle Filtering with Generative Sampling via Conditional Diffusion Modelscited by 2
  7. 2025Diffusion differentiable resamplingcited by 2
  8. 2025Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposalscited by 1
  9. 2024Differentiable Particle Filtering using Optimal Placement Resamplingcited by 0