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  1. Home
  3. On Semi-supervised Estimation Using Exponential Tilt Mixture Models.
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  3. On Semi-supervised Estimation Using Exponential Tilt Mixture Models.

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On semi-supervised estimation using exponential tilt mixture models.

Ye Tian1, Xinwei Zhang2, Zhiqiang Tan1

  • 1Department of Statistics, Rutgers University, Piscataway, NJ 08854, United States of America.

Journal of Statistical Planning and Inference
|August 21, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces exponential tilt mixture (ETM) models for semi-supervised logistic regression, improving estimation efficiency. The approach enhances statistical modeling when labeled and unlabeled data have different class proportions.

Keywords:
Asymptotic efficiencyExponential tilt mixture modelLogistic regressionMaximum likelihood estimationSemi-supervised learning

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • Semi-supervised learning leverages both labeled and unlabeled data.
  • Logistic regression is a fundamental statistical model for binary outcomes.
  • Existing methods may not fully utilize unlabeled data when class proportions differ.

Purpose of the Study:

  • To develop and analyze exponential tilt mixture (ETM) models for semi-supervised logistic regression.
  • To investigate the efficiency of ETM-based estimation compared to supervised methods.
  • To explore the impact of differing class proportions between labeled and unlabeled datasets.

Main Methods:

  • Utilized exponential tilt mixture (ETM) models.
  • Employed maximum nonparametric likelihood estimation.
  • Derived asymptotic properties of the proposed estimators.
  • Conducted simulation studies for numerical validation.

    • Main Results:

    • Demonstrated improved efficiency of ETM-based estimation over supervised logistic regression.
    • Showcased effectiveness in both random and outcome-stratified sampling setups.
    • Reconciled efficiency gains with existing semiparametric efficiency theory under specific conditions.

    Conclusions:

    • ETM models offer a statistically robust approach for semi-supervised logistic regression.
    • The method provides efficiency gains, particularly when class proportions vary.
    • Theoretical findings are supported by simulation evidence, highlighting practical applicability.