Nonparametric targeted Bayesian estimation of class proportions in unlabeled data

Area of Science:

• Statistics
• Machine Learning
• Bayesian Inference

Background:

• Estimating class proportions in unlabeled datasets is crucial for various applications.
• Existing methods may require strong assumptions or extensive data.
• Targeted learning offers a framework for efficient inference on specific parameters.

Purpose of the Study:

• To introduce a novel Bayesian estimator for class proportion in unlabeled data.
• To develop a method that requires prior specification only for the target parameter.
• To ensure the estimator yields a tightly concentrated and reliable posterior distribution.

Main Methods:

• Utilizing the targeted learning framework for Bayesian estimation.
• Specifying a prior distribution solely for the target parameter of interest.
• Proving a Bernstein-von Mises-type result to establish posterior convergence properties.

Main Results:

• The proposed Bayesian procedure yields a Gaussian, doubly robust, and efficient posterior distribution in the limit.
• The posterior distribution converges to that of an efficient, asymptotically linear estimator.
• Nuisance parameters only need to be estimated at slower-than-parametric rates.

Conclusions:

• The novel Bayesian estimator provides a robust and efficient method for estimating class proportions in unlabeled datasets.
• The targeted learning approach aligns with Bayesian subjectivism by focusing on the target parameter.
• The generalizable procedure can be adapted for estimating various pathwise differentiable parameters in non-parametric models.