Withdrawn - 14. Approximate Bayesian classifier for high-dimensional data

The Bayes classifier provides a way of performing probabilistic classification using a posterior distribution of the outcome given predictors. When there are many predictors, however, the need for estimating the high-dimensional covariance matrix, which yields prohibitively heavy computational cost, makes its applicability limited. A naive Bayes classifier is a popular alternative for handling high-dimensional data since its assumption on the conditional independence of features given class eases the burden associated with the high-dimensional covariance matrix. Despite its computational efficiency, naive Bayes classifier leads to poor statistical performance when the features are correlated, a case commonly observed in real-world data. To address such issue, we propose a new Bayesian classifier called the approximate Bayesian classifier. Our method is based on the Vecchia approximation that has played a crucial role in dimension reduction in recent Bayesian spatial modeling. To adapt the Vecchia approach for spatial modeling into a classification framework, we define the concept of neighborhood, which lies at the core of the Vacchia approximation, using the relationship between the coefficients and the correlations under the normality assumption. The performance of our proposed method is investigated via numerical studies.

Vecchia 

Mid-Level

Knowledge

Women in Statistics and Data Science 2025