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<p>As the development of measuring instruments and computers has accelerated the collection of massive amounts of data, functional data analysis (FDA) has experienced a surge of attention. The FDA methodology treats longitudinal data as a set of functions on which inference is performed. Functionalizing data typically involves fitting the data with basis functions, and the number of basis functions is chosen to be fewer than the sample size. This paper challenges this convention. Recent statistical theory has revealed the double-descent phenomenon in which overparameterization overcomes overfitting and leads to precise interpolation. Applying this idea to choosing the number of bases to be used for functional data, we show that using excess bases can achieve more accurate predictions. Specifically, we explore this phenomenon in functional regression and examine its validity through numerical experiments. In addition, we demonstrate that the double-descent occurs in two real-world datasets, confirming its importance in practical applications.</p>

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Reconciling functional data regression with excess bases

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • Tomoya Wakayama,
  • Hidetoshi Matsui

摘要

As the development of measuring instruments and computers has accelerated the collection of massive amounts of data, functional data analysis (FDA) has experienced a surge of attention. The FDA methodology treats longitudinal data as a set of functions on which inference is performed. Functionalizing data typically involves fitting the data with basis functions, and the number of basis functions is chosen to be fewer than the sample size. This paper challenges this convention. Recent statistical theory has revealed the double-descent phenomenon in which overparameterization overcomes overfitting and leads to precise interpolation. Applying this idea to choosing the number of bases to be used for functional data, we show that using excess bases can achieve more accurate predictions. Specifically, we explore this phenomenon in functional regression and examine its validity through numerical experiments. In addition, we demonstrate that the double-descent occurs in two real-world datasets, confirming its importance in practical applications.