Large Scale Assessment of Consistency in Sleep Stage Scoring Rules Among Multiple Sleep Centers Using an Interpretable Machine Learning Algorithm

Liu, Gi-Ren; Lin, Ting-Yu; Wu, Hau‐Tieng; Sheu, Yuan-Chung; Liu, Ching-Lung; Liu, Wen‐Te; Yang, Mei‐Chen; Ni, Yung-Lun; Chou, Kun-Ta; Chen, Chao-Hsien; Wu, Dean; Cui, Lan; Chiu, Kuo-Liang; Chiu, Hwa‐Yen; Lo, Yu‐Lun

doi:10.2139/ssrn.3544851

Cited by 3 publications

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“…The scattering transform (ST) is motivated by establishing a mathematical foundation of the convolutional neural network [20], and it has been applied to various signals, for example, fetal heart rate [8], brain waves [15,14], respiration [29], marine bioacoustics [4], and audio [1,13]. It provides a variety of representations for a given function X through a sequential interlacing convolution and nonlinear operators: where M ∈ N is the depth of ST, {j 1 , j 2 , .…”

Section: Introductionmentioning

confidence: 99%

“…In the appendix, these properties are described in more concrete terms for the possible interest of readers. On the other hand, note that there are many time series that can be modeled by random processes; for example, fetal heart rate [8], brain waves [15,14], respiration [29], marine bioacoustics [4], and audio [1,13]. While ST has been successfully applied to these signals that can be modeled by random processes, to our knowledge, there are limited theoretical results available to guide data analysts.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic analysis of higher-order scattering transform of Gaussian processes

Liu

Sheu

2022

Electron. J. Probab.

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We analyze the scattering transform with the quadratic nonlinearity (STQN) of Gaussian processes without depth limitation. STQN is a nonlinear transform that involves a sequential interlacing convolution and nonlinear operators, which is motivated to model the deep convolutional neural network. We prove that with a proper normalization, the output of STQN converges to a chi-square process with one degree of freedom in the finite dimensional distribution sense, and we provide a total variation distance control of this convergence at each time that converges to zero at an exponential rate.To show these, we derive a recursive formula to represent the intricate nonlinearity of STQN by a linear combination of Wiener chaos, and then apply the Malliavin calculus and Stein's method to achieve the goal.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of higher-order scattering transform of Gaussian processes

Liu

Sheu

2022

Electron. J. Probab.

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“…For the purpose of feature extraction, the second-order scattering transforms (ST) has been applied to various signals, for example, fetal heart rate [1], brain waves [2,3], respiration [4], marine bioacoustics [5], and audio [6,7]. Given a signal X, the second-order ST of X is defined through the convolution and modulus operators as follows where ψ j 1 (•) = 2 −j 1 ψ(2 −j 1 •) and ψ j 2 (•) = 2 −j 2 ψ(2 −j 2 •) are wavelets generated from a selected mother wavelet ψ.…”

Section: Introductionmentioning

confidence: 99%

When Scattering Transform Meets Non-Gaussian Random Processes, a Double Scaling Limit Result

Liu¹,

Sheu²,

Wu³

2021

Preprint

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We explore the finite dimensional distributions of the second-order scattering transform of a class of non-Gaussian processes when all the scaling parameters go to infinity simultaneously. For frequently used wavelets, we find a coupling rule for the scale parameters of the wavelet transform within the first and second layers such that the limit exists. The coupling rule is explicitly expressed in terms of the Hurst index of the long range dependent inputs. More importantly, the spectral density function of the limiting process can be explicitly expressed in terms of the Hurst index of the long-range dependent input process and the Fourier transform of the mother wavelet. To obtain these results, we first show that the scattering transform of a class of non-Gaussian processes can be approximated by the second-order scattering transform of Gaussian processes when the scale parameters are sufficiently large. Secondly, for each approximation process, which is still a non-Gaussian random process, we show that its doubling scaling limit exists by the moment method. The long-range dependent non-Gaussian model considered in this work is realized by real data, and assumptions are supported by numerical results.

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“…The scattering transform (ST) is motivated by establishing a mathematical foundation of the convolutional neural network [1], and it has been applied to various signals, for example, fetal heart rate [2], brain waves [3,4], respiration [5], marine bioacoustics [6], and audio [7,8]. It provides a variety of representations for a given function X through a sequential interlacing convolution and nonlinear operators:…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis of Higher-order Scattering Transform of Gaussian Processes

Liu¹,

Sheu²,

Wu³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We analyze the scattering transform with the quadratic nonlinearity (STQN) of Gaussian processes without depth limitation. STQN is a nonlinear transform that involves a sequential interlacing convolution and nonlinear operators, which is motivated to model the deep convolutional neural network. We prove that with a proper normalization, the output of STQN converges to a chi-square process with one degree of freedom in the finite dimensional distribution sense, and we provide a total variation distance control of this convergence at each time that converges to zero at an exponential rate. To show these, we derive a recursive formula to represent the intricate nonlinearity of STQN by a linear combination of Wiener chaos, and then apply the Malliavin calculus and Stein's method to achieve the goal.

show abstract

Large Scale Assessment of Consistency in Sleep Stage Scoring Rules Among Multiple Sleep Centers Using an Interpretable Machine Learning Algorithm

Cited by 3 publications

References 0 publications

Asymptotic analysis of higher-order scattering transform of Gaussian processes

Asymptotic analysis of higher-order scattering transform of Gaussian processes

When Scattering Transform Meets Non-Gaussian Random Processes, a Double Scaling Limit Result

Asymptotic Analysis of Higher-order Scattering Transform of Gaussian Processes

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