Coefficient-based regularized distribution regression

Mao, Yuan; Shi, Lei; Guo, Zheng-Chu

doi:10.1016/j.jat.2023.105995

Cited by 1 publication

(1 citation statement)

References 24 publications

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“…Another interesting topic is to design spectral algorithms for functional inputs and outputs and establish convergence analysis under the framework of operator regression [19]. It is also of great interest to investigate distributed spectral algorithms [10,11], distribution regression [18], robust online learning [8] and deep learning algorithms [22,23] for functional regression models.…”

Section: Proof Of Main Resultsmentioning

confidence: 99%

Spectral algorithms for functional linear regression

Fan,

Guo,

Shi

2024

CPAA

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Spectral algorithms offer a general and flexible framework for a broad range of machine learning problems and have attracted considerable attention recently. However, the theoretical properties of these algorithms are still largely unknown for infinite-dimensional functional data learning. To fill this void, we study the performance of spectral algorithms for functional linear regression within the framework of reproducing kernel Hilbert space. Despite the generality of the proposed methods, we show that they are easily implementable and can attain minimax rates of convergence for prediction in terms of regularity of the slope function, eigenvalue decay rate of the integral operator determined by both the reproducing kernel and the covariance kernel, and qualification of the filter function of the spectral algorithm. In addition, our analysis also pinpoints the benefits of spectral algorithms in overcoming the saturation effect of roughness regularization methods.

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