Optimal estimation for Functional Linear Regression with Noisy Discretized Data

• URL: http://arxiv.org/abs/2609.08671v1
• Date: Tue, 08 Sep 2026 12:37:10 GMT
• Title: Optimal estimation for Functional Linear Regression with Noisy Discretized Data
• Abstract summary: The underlying curves are reconstructed from the discrete noisy observations.<n>The slope function is estimated by a penalized least-squares criterion over finite-dimensional trigonometric spaces.<n>The proposed method is illustrated on simulated data and on a real meteorological dataset.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we consider the scalar-on-function linear regression model under a realistic sampling scheme in which the functional covariates are observed on a regular grid and contaminated by additive noise. We propose a two-step estimation procedure: first, the underlying curves are reconstructed from the discrete noisy observations using a Fourier-based projection method; second, the slope function is estimated by a penalized least-squares criterion over finite-dimensional trigonometric spaces, with data-driven selection of the model dimension. We establish oracle-type inequalities for the prediction error, both with respect to the reconstructed curves and to the true latent curves. Under regularity assumptions on the slope function and polynomial decay of the eigenvalues of the covariate, we derive convergence rates for the prediction error and show that our estimator attains the minimax rate when the number of grid points is sufficiently large. Finally, the proposed method is illustrated on simulated data and on a real meteorological dataset.

Related papers

• Functional linear regression from sparse to dense designs: a pooling-ridge method and minimax optimality [0.962543698736491]
  Functional data analysis is an important statistical field that treats data as random functions.<n>In practice, the random functions are often not fully observed but instead measured at discrete times.<n>We propose a novel approach, referred to as pooling ridge estimation, which combines the advantages of pooling strategy and RKHS-based method.
  arXiv  Detail & Related papers  (2026-08-26T07:36:39Z)
• Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Models [1.1458853556386799]
  We consider the problem of scalable sampling algorithms to fit generalized linear mixed models on large datasets.<n>We advocate the use of a mirror Langevin dynamics algorithm based on data subsampling and provide concrete guidelines for its use in an inference framework.
  arXiv  Detail & Related papers  (2026-04-28T18:11:19Z)
• Dynamical local Fréchet curve regression in manifolds [0.0]
  We consider the prediction problem of the Earth's magnetic field from the time-varying geocentric latitude and longitude of NASA's MAGSAT spacecraft.<n>As motivating real data application, we consider the prediction problem of the Earth's magnetic field from the time-varying geocentric latitude and longitude of the satellite NASA's MAGSAT spacecraft.
  arXiv  Detail & Related papers  (2025-05-08T12:06:59Z)
• Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models [76.52307406752556]
  We derive a novel deterministic equivalence for the two-point function of a random resolvent.<n>We give a unified derivation of the performance of a wide variety of high-dimensional trained linear models with gradient descent.
  arXiv  Detail & Related papers  (2025-02-07T16:45:40Z)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions.<n>For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling.<n>We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent [43.097493761380186]
  gradient algorithms are an efficient method of approximately solving linear systems. We show that gradient descent produces accurate predictions, even in cases where it does not converge quickly to the optimum. Experimentally, gradient descent achieves state-of-the-art performance on sufficiently large-scale or ill-conditioned regression tasks.
  arXiv  Detail & Related papers  (2023-06-20T15:07:37Z)
• Refining Amortized Posterior Approximations using Gradient-Based Summary Statistics [0.9176056742068814]
  We present an iterative framework to improve the amortized approximations of posterior distributions in the context of inverse problems. We validate our method in a controlled setting by applying it to a stylized problem, and observe improved posterior approximations with each iteration.
  arXiv  Detail & Related papers  (2023-05-15T15:47:19Z)
• Modeling High-Dimensional Data with Unknown Cut Points: A Fusion Penalized Logistic Threshold Regression [2.520538806201793]
  In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. We consider a threshold model that all continuous features are discretized into ordinal levels, which further determine the binary responses. We find the lasso model is well suited in the problem of early detection and prediction for chronic disease like diabetes.
  arXiv  Detail & Related papers  (2022-02-17T04:16:40Z)
• Time varying regression with hidden linear dynamics [74.9914602730208]
  We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates.
  arXiv  Detail & Related papers  (2021-12-29T23:37:06Z)
• Heavy-tailed Streaming Statistical Estimation [58.70341336199497]
  We consider the task of heavy-tailed statistical estimation given streaming $p$ samples. We design a clipped gradient descent and provide an improved analysis under a more nuanced condition on the noise of gradients.
  arXiv  Detail & Related papers  (2021-08-25T21:30:27Z)
• Near-optimal inference in adaptive linear regression [60.08422051718195]
  Even simple methods like least squares can exhibit non-normal behavior when data is collected in an adaptive manner. We propose a family of online debiasing estimators to correct these distributional anomalies in at least squares estimation. We demonstrate the usefulness of our theory via applications to multi-armed bandit, autoregressive time series estimation, and active learning with exploration.
  arXiv  Detail & Related papers  (2021-07-05T21:05:11Z)
• Path Sample-Analytic Gradient Estimators for Stochastic Binary Networks [78.76880041670904]
  In neural networks with binary activations and or binary weights the training by gradient descent is complicated. We propose a new method for this estimation problem combining sampling and analytic approximation steps. We experimentally show higher accuracy in gradient estimation and demonstrate a more stable and better performing training in deep convolutional models.
  arXiv  Detail & Related papers  (2020-06-04T21:51:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.