Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems
Authors: Dengfei Zeng, Lijian Jiang, Shuyu Sun et al.
Summary
arXiv:2605. 13174v1 Announce Type: new Abstract: A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables.
Relevance
Read next because Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Training one persona to emit a [ZLT] marker without bystanders adopting it has a one-cell-wide LR x epochs window on Qwen2.5-7B-Instruct (LOW confidence)", clean result "A pretraining-data-poisoned Qwen3-4B backdoor only fires on the exact trigger tokens — paraphrases don't activate it, and base-model similarity to the trigger doesn't predict which inputs fire (MODERATE confidence)". Matching terms: rect, training, line, rate, coupling, collapse. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.13174v1 Announce Type: new Abstract: A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the minimization of the maximum mean discrepancy (MMD) between the true joint measure and its transport-based approximation. To circumvent the non-convexity in the MMD optimization, we introduce a training-free transport filter method via gradient flows, which leads to an analytic computation for the transport map that implies the steepest descent direction of the MMD. The proposed approach accurately approximates non-Gaussian filtering posteriors and avoids particle collapse. We provide a convergence analysis for the expectation of the MMD between the approximated posterior and the truth posterior. Finally, we extend the method to high-dimensional problems through domain localization. Numerical examples demonstrate the superior performance of our approach over conventional filtering methods in nonlinear, non-Gaussian scenarios.