An Empirical Bayes Approach for High Dimensional Classification
This work addresses classification challenges in high-dimensional data, though it appears incremental as it builds on existing empirical Bayes and variational methods.
The authors tackled high-dimensional classification by developing an empirical Bayes estimator using Dirichlet process mixture models to estimate sparse normalized mean differences, achieving theoretical connections between estimation error and misclassification error while providing a computationally efficient variational Bayes algorithm.
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a bridge to connect the estimation error of the mean difference and the misclassification error, also provide sufficient conditions of sub-optimal classifiers and optimal classifiers. In implementation, a variational Bayes algorithm is developed to compute the posterior efficiently and could be parallelized to deal with the ultra-high dimensional case.