Online gradient descent algorithms for functional data learning

Xiaming Chen, Bohao Tang, Jun Fan (Corresponding Author), Xin Guo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


Functional linear model is a fruitfully applied general framework for regression problems, including those with intrinsically infinite-dimensional data. Online gradient descent methods, despite their evidenced power of processing online or large-sized data, are not well studied for learning with functional data. In this paper, we study reproducing kernel-based online learning algorithms for functional data, and derive convergence rates for the expected excess prediction risk under both online and finite-horizon settings of step-sizes respectively. It is well understood that nontrivial uniform convergence rates for the estimation task depend on the regularity of the slope function. Surprisingly, the convergence rates we derive for the prediction task can assume no regularity from slope. Our analysis reveals the intrinsic difference between the estimation task and the prediction task in functional data learning.

Original languageEnglish
Article number101635
Pages (from-to)1-14
Number of pages14
JournalJournal of Complexity
Early online dateDec 2021
Publication statusPublished - Jun 2022


  • Error analysis
  • Gradient descent
  • Learning theory
  • Online learning
  • Reproducing kernel Hilbert space

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • General Mathematics
  • Control and Optimization
  • Applied Mathematics


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