Kernel Variational Inference Flow for Nonlinear Filtering Problem

2025/09/23 by Weiye Gan, Gan, Weiye, Zhijun Zeng +5
Computer Science · Physics and Astronomy · #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.2509.18589

openalex publication_date 2025/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a novel particle flow for sampling called kernel variational inference flow (KVIF). KVIF do not require the explicit formula of the target distribution which is usually unknown in filtering problem. Therefore, it can be applied to construct filters with higher accuracy in the update stage. Such an improvement has theoretical assurance. Some numerical experiments for comparison with other classical filters are also demonstrated.

Citations

• Split Gibbs Discrete Diffusion Posterior Sampling
• Semi-Implicit Functional Gradient Flow for Efficient Sampling
• Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent
• Particle-based Variational Inference with Generalized Wasserstein Gradient Flow
• Particle-based Variational Inference with Preconditioned Functional Gradient Flow
• A Finite-Particle Convergence Rate for Stein Variational Gradient Descent
• Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Condition
• Variational Wasserstein gradient flow
• Neural Variational Gradient Descent
• A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1
• A Non-Asymptotic Analysis for Stein Variational Gradient Descent
• SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
• On the geometry of Stein variational gradient descent
• A Unified Particle-Optimization Framework for Scalable Bayesian Sampling
• Learning to Draw Samples with Amortized Stein Variational Gradient Descent
• Stein Variational Policy Gradient
• Stein Variational Gradient Descent: A General Purpose Bayesian Inference\n Algorithm
• Variational Inference: A Review for Statisticians
• Real Time Solution of the Nonlinear Filtering Problem without Memory II
• Particle Filters in Robotics (Invited Talk)

Related

• Variational Formulation of the Particle Flow Particle Filter
• Stochastic Particle Flow for Nonlinear High-Dimensional Filtering Problems
• Particle-based Variational Inference with Preconditioned Functional Gradient Flow
• Semi-Implicit Functional Gradient Flow for Efficient Sampling
• Variational Rejection Particle Filtering