Learning the smoothness of noisy curves with application to online curve estimation

2020/09/30 by Steven Golovkine, Nicolas Klutchnikoff, Valentin Patilea · 12 citations
Computer Science · Mathematics · #Anomaly Detection Techniques and Applications #Applied mathematics #Computer science #Differentiable function #Estimator #Gaussian Processes and Bayesian Inference #Mathematical analysis #Mathematical optimization #Mathematics #Pointwise #Polynomial #Set (abstract data type) #Smoothness #Statistical Methods and Inference #Statistics #math.ST #msc:62G05 #msc:62M09 #msc:62R10 #stat.TH

paper · pdf · open access · doi:10.1214/22-ejs1997

published in Electronic Journal of Statistics 16(1) (Institute of Mathematical Statistics)

openalex created_date 2020/09/14 · openalex publication_date 2022/01/01 · arxiv created 2022/03/14 · arxiv updated 2022/03/15 · openalex updated_date 2026/08/05

Abstract

Combining information both within and across trajectories, we propose a simple estimator for the local regularity of the trajectories of a stochastic process. Independent trajectories are measured with errors at randomly sampled time points. Non-asymptotic bounds for the concentration of the estimator are derived. Given the estimate of the local regularity, we build a nearly optimal local polynomial smoother from the curves from a new, possibly very large sample of noisy trajectories. We derive non-asymptotic pointwise risk bounds uniformly over the new set of curves. Our estimates perform well in simulations. Real data sets illustrate the effectiveness of the new approaches.

Citations

• Review of Functional Data Analysis
• Estimation of fractal dimension for a class of non-Gaussian stationary processes and fields
• Confidence bands in density estimation
• Model-Based Clustering, Discriminant Analysis, and Density Estimation
• Estimation of the Hurst parameter from discrete noisy data
• A Framework for Probabilistic Generic Traffic Scene Prediction
• Model-Predictive Policy Learning with Uncertainty Regularization for Driving in Dense Traffic

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