Nonlinear function on function additive model with multiple predictor curves

Qi, Xin; Luo, Ruiyan

doi:10.5705/ss.202017.0249

Cited by 8 publications

(5 citation statements)

References 28 publications

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“…However, as pointed out by Müller and Yao (2008), linear relations may not be adequate to characterize dependence of one random function on another function in some applications. The Hawaii ocean data set studied in Qi and Luo (2019) justified this statement. Nonlinear function-on-function regression models have received substantially less attention in FDA (Reimherr et al, 2018), let alone statistical inference of such models.…”

Section: Introductionmentioning

confidence: 62%

Nonlinear function-on-function regression by RKHS

Sang¹,

Li²

2022

Preprint

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We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the functional covariate and the functional response, and then build a second-layer Hilbert space for the covariate to capture nonlinearity. The second-layer space is assumed to be a reproducing kernel Hilbert space, which is generated by a positive definite kernel determined by the inner product of the first-layer Hilbert space for X-this structure is known as the nested Hilbert spaces. We develop estimation procedures to implement the proposed method, which allows the functional data to be observed at different time points for different subjects. Furthermore, we establish the convergence rate of our estimator as well as the weak convergence of the predicted response in the Hilbert space. Numerical studies including both simulations and a data application are conducted to investigate the performance of our estimator in finite sample.

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Section: Introductionmentioning

confidence: 62%

Nonlinear function-on-function regression by RKHS

Sang¹,

Li²

2022

Preprint

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“…Based on the data of 3D medical image information framework and image overlapping information model, this paper uses data mining algorithm and machine learning algorithm to detect 3D medical image information, analyzes the advantages of data mining algorithm and machine learning algorithm in medical image overlapping area information detection, and establishes the nonlinear function expression of 3D medical image overlapping area, 15 realize the detection of 3D medical image information.…”

Section: Detection Of Overlapped Area Information On 3d Medical Image...mentioning

confidence: 99%

Research on 3D medical image surface reconstruction based on data mining and machine learning

Hua

Liu

Yin

et al. 2021

Int J of Intelligent Sys

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Three-dimensional (3D) medical images are prone to overlap, and there are some problems, such as low detection efficiency and inconsistent with the actual situation. Therefore, a 3D medical image surface reconstruction method based on data mining and machine learning is proposed. The 3D medical images were classified according to different ways, the information frame of 3D medical images was established and the surface overlapping information model of 3D images was given. Based on this information framework, the nonlinear function of overlapping area information of 3D medical images was constructed. The weight of the nonlinear function was used to calculate the input and output results of overlapping area information. Combined with the input mode of 3D medical image information, the error between the information output and the expected output was set. The nonlinear function weight of the overlapping area information of 3D medical images was modified by using the learning rate and the use time of the overlapping area information, and the influence factors of the overlapping information detection were obtained by increasing the situation terms, so as to complete the detection of the surface reconstruction information of 3D medical images. The experimental results show that

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“…Moreover, [Wan14] studied mixed effect and [LQ19] studied interaction effect in linear function-on-function model. In addition to linear function-on-function regression, [QL19] and [SSG15] studied functional additive models, but there is no theoretical result about variable selection in high-dimensional setting.…”

Section: Related Workmentioning

confidence: 99%

High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach

Zhao¹,

Zhai²,

Wang³

et al. 2021

Preprint

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Undirected graphical models have been widely used to model the conditional independence structure of high-dimensional random vector data for years. In many modern applications such as EEG and fMRI data, the observations are multivariate random functions rather than scalars. To model the conditional independence of this type of data, functional graphical models are proposed and have attracted an increasing attention in recent years. In this paper, we propose a neighborhood selection approach to estimate Gaussian functional graphical models. We first estimate the neighborhood of all nodes via function-on-function regression, and then we can recover the whole graph structure based on the neighborhood information. By estimating conditional structure directly, we can circumvent the need of a well-defined precision operator which generally does not exist. Besides, we can better explore the effect of the choice of function basis for dimension reduction. We give a criterion for choosing the best function basis and motivate two practically useful choices, which we justified by both theory and experiments and show that they are better than expanding each function onto its own FPCA basis as in previous literature. In addition, the neighborhood selection approach is computationally more efficient than fglasso as it is more easy to do parallel computing. The statistical consistency of our proposed methods in high-dimensional setting are supported by both theory and experiment.

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Nonlinear function on function additive model with multiple predictor curves

Cited by 8 publications

References 28 publications

Nonlinear function-on-function regression by RKHS

Nonlinear function-on-function regression by RKHS

Research on 3D medical image surface reconstruction based on data mining and machine learning

High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach

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