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Semi-supervised inference for nonparametric logistic regression.

Tong Wang1, Wenlu Tang2, Yuanyuan Lin1

  • 1Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong.

Statistics in Medicine
|May 10, 2023
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Summary
This summary is machine-generated.

This study introduces a novel semi-supervised method for nonparametric logistic regression using spline techniques. The approach enhances estimation efficiency by leveraging unlabeled data alongside limited labeled case-control data.

Keywords:
case-control studiesnonparametric logistic regressionsemi-supervised inference

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Area of Science:

  • Statistics
  • Machine Learning

Background:

  • Semi-supervised learning is crucial when labeled data is scarce and expensive to obtain.
  • Nonparametric logistic regression is vital for modeling complex relationships between predictors and binary outcomes.
  • Case-control sampling is common in epidemiological studies but presents unique statistical challenges.

Purpose of the Study:

  • To develop an efficient semi-supervised estimator for nonparametric logistic regression.
  • To address challenges in estimating regression functions when only limited labeled case-control data and abundant unlabeled data are available.
  • To improve upon traditional supervised methods by incorporating unlabeled data.

Main Methods:

  • A two-stage nonparametric semi-supervised estimation approach is proposed.
  • Spline-based methods are utilized for function estimation.
  • The first stage estimates the density function using unlabeled data, which informs the second stage's likelihood maximization for the labeled case-control data.

Main Results:

  • The proposed semi-supervised two-stage estimator demonstrates consistency and functional asymptotic normality under mild conditions.
  • The method effectively utilizes unlabeled data to achieve more efficient estimation compared to supervised methods.
  • Simulation studies confirm the superior performance of the proposed approach.

Conclusions:

  • The developed semi-supervised method offers a statistically sound and efficient way to perform nonparametric logistic regression.
  • Leveraging unlabeled data significantly enhances the estimation of the target regression function.
  • The approach is applicable to real-world scenarios, such as the analyzed skin segmentation data.