Enhancing Naive Bayes Algorithm with Stable Distributions for Classification

The Naive Bayes (NB) algorithm is widely recognized for its efficiency and simplicity in classification tasks, particularly in domains with high-dimensional data. While the Gaussian Naive Bayes (GNB) model assumes a Gaussian distribution for continuous features, this assumption often limits its applicability to real-world datasets with non-Gaussian characteristics. To address this limitation, we introduce an enhanced Naive Bayes framework that incorporates stable distributions to model feature distributions. Stable distributions, with their flexibility in handling skewness and heavy tails, provide a more realistic representation of diverse data characteristics. This paper details the theoretical integration of stable distributions into the NB algorithm, the implementation process utilizing R and Python, and an experimental evaluation across multiple datasets. Results indicate that the proposed approach offers competitive or superior classification accuracy, particularly when the Gaussian assumption is violated, underscoring its potential for practical applications in diverse fields.