Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2503.15160

Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling

Yoonsang Lee
View original source ↗Read source document ↗Export metadata ↓

Abstract

Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is first denoised via a standard Kalman update, while the unobserved component is estimated using a nonlinear regression approach based on kernel density estimation. The method incorporates a subsampling strategy to ensure stability and, when necessary, employs unsupervised clustering to refine the conditional estimate. Numerical experiments on Lorenz systems and a PDE-constrained inverse problem illustrate that the proposed nonlinear update can reduce estimation errors compared to standard linear updates, especially in highly nonlinear scenarios.

Explore related subjects

stat.MLmath.PRmath.STstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yoonsang Lee. 2025-03-19. Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling. https://arxiv.org/abs/2503.15160

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

MultiwayPAM: Multiway Partitioning Around Medoids for LLM-as-a-Judge Score Analysis

LLM-as-a-Judge is a flexible framework for text evaluation, which allows us to obtain scores for the quality of a given text from various perspectives by changing the prompt template. Two main challenges in using LLM-as-a-Judge are computational cost of inference using a large language model (LLM), especially when evaluating a large number of instances, and inherent bias of an LLM evaluator. To address these issues and reveal the structure of score bias caused by an LLM evaluator, we propose to apply a tensor clustering method to a given LLM-as-a-Judge score tensor, whose entries are the scores for different combinations of questions, answerers, and evaluators. Specifically, we develop a new tensor clustering method MultiwayPAM, with which we can simultaneously estimate the cluster membership and the medoids for each mode of a given data tensor. By observing the medoids obtained by MultiwayPAM, we can gain knowledge about the membership of each question/answerer/evaluator cluster. We experimentally show the effectiveness of MultiwayPAM by applying it to the score tensors for two practical datasets.

stat.ML↗
arXiv2026

Learning to Fluctuate: Statistical Foundations for Causal Tabular Pretraining

Causal tabular foundation models amortize effect estimation across synthetic mechanisms, but latent-effect supervision rewards posterior shrinkage rather than encoding the repeated-sample response needed in a fixed deployment population. We introduce fluctuation-supervised pretraining (FSP): each synthetic table is labeled by its average treatment effect plus its efficient influence-function fluctuation; deployment remains a frozen forward pass. Along the path $T_{λ,P}=θ(P)+λP_nψ_P$, we prove an endpoint transition: every fixed $λ<1$ retains label ambiguity of order $(1-λ)^2/n$, whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order $n^{-2}$. A finite-pretraining bound combines label, network, episode-sampling, and optimization errors; its sampling defect controls fixed-mechanism bias, mean squared error, variance, Gaussian approximation, and, with variance-head accuracy, studentized coverage. Complementary lower bounds separate local $n^{-1}$ ATE risk from the $\log N/M$ excess risk of generic finite-dictionary episode learning. Experiments trace the learned sampling response. Across 24 nonlinear continuous-covariate cells at trained context lengths, continuous-row FSP lowers checkpoint-mean macro RMSE by 7.0% versus S-learner and wins all 12 weak-overlap cells; validation-selected Summary FSP deploys $11.6\times$ faster per table in our warm one-thread benchmark. Under effect shift, matched Raw FSP lowers mean-checkpoint RMSE by 54.2% and teacher defect by 99.0% versus latent-effect supervision, and RMSE by 10.2% versus the released CausalPFN-S checkpoint. Known-effect semisynthesis tests coverage; two randomized-study evaluations show that lower RMSE can coexist with residual attenuation.

stat.ML↗
arXiv2026

Personalised federated learning for Riemannian and Euclidean EEG decoding

Federated learning (FL) lets EEG decoders learn from recordings of several subjects without pooling them. We consider two light EEG decoders, the Riemannian SPDNet and the Euclidean EEGNet. Both split into a trunk, which builds a latent representation, and a head, which classifies it. Inter-subject variability, however, makes a single shared FL model a poor fit for each subject. Personalised FL addresses this: all subjects learn a common trunk, and each subject keeps its own head. We adapt it for SPDNet and study its effects against standard FL and centralised training, with EEGNet as a Euclidean baseline. Experiments cover three motor-imagery datasets that span diverse regimes in channels, subjects and classes. We observe that personalised SPDNet reaches higher accuracy than both standard FL and centralised training, while converging in fewer rounds and communicating fewer parameters than standard FL. It also outperforms every EEGNet configuration on two of the three datasets, although centralised EEGNet outperforms centralised SPDNet.

stat.ML↗