Finite-sample analysis of impacts of unlabeled data and their labeling mechanisms in linear discriminant analysis

ABSTRACT

It is widely believed that unlabeled data are promising for improving prediction accuracy in classification problems. Although theoretical studies about when/how unlabeled data are beneficial exist, an actual prediction improvement has not been sufficiently investigated for a finite sample in a systematic manner. We investigate the impact of unlabeled data in linear discriminant analysis and compare the error rates of the classifiers estimated with/without unlabeled data. Our focus is a labeling mechanism that characterizes the probabilistic structure of occurrence of labeled cases. Results imply that an extremely small proportion of unlabeled data has a large effect on the analysis results.

Keywords:

• Classification error
• Missing data
• Monte Carlo simulation
• Relative efficiency
• Semi-supervised learning

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H30
• 68T10
• 62F12

Acknowledgment

The authors would like to acknowledge the associate editor and anonymous reviewers for their helpful comments and suggestions.

Funding

K. Hayashi is supported by JSPS KAKENHI (Grant-in-Aid for Scientific Research) grant number 24700276. K. Takai is supported by JSPS KAKENHI (Grant-in-Aid for Scientific Research) grant number 20572019.

Notes

1 To be precise, this quantity should be called “non-MCAR-ness.” However, for simplicity we call this “MCAR-ness.”