# Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering

arXiv: https://arxiv.org/abs/1501.02056 · HTML: https://mlsanity.com/paper/1501.02056/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2015.

## Built on by (most cited first, 22 of 22)

- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Generalized Kernel Thinning](https://mlsanity.com/paper/2110.01593/) (2021)
- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Sampling](https://mlsanity.com/paper/2311.13548/) (2023)
- [Fast Private Kernel Density Estimation via Locality Sensitive Quantization](https://mlsanity.com/paper/2307.01877/) (2023)
- [Interaction-Force Transport Gradient Flows](https://mlsanity.com/paper/2405.17075/) (2024)
- [A Dictionary of Closed-Form Kernel Mean Embeddings](https://mlsanity.com/paper/2504.18830/) (2025)
- [Heavy Ball Momentum for Conditional Gradient](https://mlsanity.com/paper/2110.04243/) (2021)
- [When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality](https://mlsanity.com/paper/2305.16527/) (2023)
- [No Dimensional Sampling Coresets for Classification](https://mlsanity.com/paper/2402.05280/) (2024)
- [Compressed Monte Carlo with application in particle filtering](https://mlsanity.com/paper/2107.08459/) (2021)
- [Sparse solutions of the kernel herding algorithm by improved gradient approximation](https://mlsanity.com/paper/2105.07900/) (2021)
- [Sequence Modeling with Spectral Mean Flows](https://mlsanity.com/paper/2510.15366/) (2025)
- [Stronger Coreset Bounds for Kernel Density Estimators via Chaining](https://mlsanity.com/paper/2310.08548/) (2023)
- [New Bounds for Kernel Sums via Fast Spherical Embeddings](https://mlsanity.com/paper/2605.01263/) (2026)
- [Continuous Herded Gibbs Sampling](https://mlsanity.com/paper/2106.06430/) (2021)
- [Screening for a Reweighted Penalized Conditional Gradient Method](https://mlsanity.com/paper/2107.01106/) (2021)
- [Approximate Bayesian Computation Based on Maxima Weighted Isolation Kernel Mapping](https://mlsanity.com/paper/2201.12745/) (2022)
- [Reinforcement Learning for Control of Evolutionary and Ecological Processes](https://mlsanity.com/paper/2305.03340/) (2023)
- [Dimension-Independent Kernel ε-Covers](https://mlsanity.com/paper/2306.16516/) (2023)
- [Deterministic Fokker-Planck Transport -- With Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlo](https://mlsanity.com/paper/2410.18993/) (2024)
- [Convex-Geometric Error Bounds for Positive-Weight Kernel Quadrature](https://mlsanity.com/paper/2605.05705/) (2026)

## Abstract (arXiv)

Recently, the Frank-Wolfe optimization algorithm was suggested as a procedure to obtain adaptive quadrature rules for integrals of functions in a reproducing kernel Hilbert space (RKHS) with a potentially faster rate of convergence than Monte Carlo integration (and "kernel herding" was shown to be a special case of this procedure). In this paper, we propose to replace the random sampling step in a particle filter by Frank-Wolfe optimization. By optimizing the position of the particles, we can obtain better accuracy than random or quasi-Monte Carlo sampling. In applications where the evaluation of the emission probabilities is expensive (such as in robot localization), the additional computational cost to generate the particles through optimization can be justified. Experiments on standard synthetic examples as well as on a robot localization task indicate indeed an improvement of accuracy over random and quasi-Monte Carlo sampling.