Deep non-parametric logistic model with case-control data and external summary information

Fuente: arXiv
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Auteurs principaux: Shi, Hengchao, Zheng, Ming, Yu, Wen
Format: Preprint
Publié: 2024
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_version_ 1866913490735726592
author Shi, Hengchao
Zheng, Ming
Yu, Wen
author_facet Shi, Hengchao
Zheng, Ming
Yu, Wen
contents The case-control sampling design serves as a pivotal strategy in mitigating the imbalanced structure observed in binary data. We consider the estimation of a non-parametric logistic model with the case-control data supplemented by external summary information. The incorporation of external summary information ensures the identifiability of the model. We propose a two-step estimation procedure. In the first step, the external information is utilized to estimate the marginal case proportion. In the second step, the estimated proportion is used to construct a weighted objective function for parameter training. A deep neural network architecture is employed for functional approximation. We further derive the non-asymptotic error bound of the proposed estimator. Following this the convergence rate is obtained and is shown to reach the optimal speed of the non-parametric regression estimation. Simulation studies are conducted to evaluate the theoretical findings of the proposed method. A real data example is analyzed for illustration.
format Preprint
id arxiv_https___arxiv_org_abs_2409_01829
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Deep non-parametric logistic model with case-control data and external summary information
Shi, Hengchao
Zheng, Ming
Yu, Wen
Machine Learning
62D05, 62J12
The case-control sampling design serves as a pivotal strategy in mitigating the imbalanced structure observed in binary data. We consider the estimation of a non-parametric logistic model with the case-control data supplemented by external summary information. The incorporation of external summary information ensures the identifiability of the model. We propose a two-step estimation procedure. In the first step, the external information is utilized to estimate the marginal case proportion. In the second step, the estimated proportion is used to construct a weighted objective function for parameter training. A deep neural network architecture is employed for functional approximation. We further derive the non-asymptotic error bound of the proposed estimator. Following this the convergence rate is obtained and is shown to reach the optimal speed of the non-parametric regression estimation. Simulation studies are conducted to evaluate the theoretical findings of the proposed method. A real data example is analyzed for illustration.
title Deep non-parametric logistic model with case-control data and external summary information
topic Machine Learning
62D05, 62J12
url https://arxiv.org/abs/2409.01829