On semi-supervised estimation using exponential tilt mixture models

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.