Decision-directed multivariate empirical bayes classification with nonstationary priors

Area of Science:

• Machine Learning
• Statistical Inference
• Pattern Recognition

Background:

• Adaptive classification rules require accurate estimation of prior distributions.
• Time-varying prior distributions pose a significant challenge for traditional methods.
• Empirical Bayes methods offer a framework for incorporating prior knowledge.

Purpose of the Study:

• To develop a recursive learning strategy for estimating time-varying prior distributions.
• To improve the performance of multivariate empirical Bayes adaptive classification rules.
• To address the challenge of tracking evolving data characteristics.

Main Methods:

• Formulating the prior distribution as a finite-state vector Markov chain.
• Utilizing past decisions to estimate the Markov chain's state evolution.
• Implementing a recursive nonlinear estimator for the decision process rate vector.
• Employing Doob decomposition and nonlinear least squares estimation.

Main Results:

• The proposed decision-directed learning strategy effectively tracks time-varying prior distributions.
• The recursive nonlinear estimator accurately estimates the rate vector of the decision process.
• Monte Carlo simulations demonstrate the estimator's performance.

Conclusions:

• The developed strategy provides an effective solution for adaptive classification with dynamic priors.
• This approach enhances the robustness and accuracy of empirical Bayes classifiers.
• The method is suitable for applications where data distributions evolve over time.