Sparse Quadratic Discriminant Analysis and Community Bayes
This work addresses the need for interpretable models in classification tasks, though it appears incremental as it builds on existing methods like group lasso and extends them to community-based partitioning.
The paper tackles the challenge of interpretable classification by developing a method that spans quadratic discriminant analysis and naive Bayes using sparse graphical models, achieving interpretable models through sparsity patterns and partitioning features into independent communities to simplify classification.
We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of sparsity across precision matrices. It gives sparse estimates of interactions and produces interpretable models. Inspired by the connected-components structure of the estimated precision matrices, we propose the community Bayes model, which partitions features into several conditional independent communities and splits the classification problem into separate smaller ones. The community Bayes idea is quite general and can be applied to non-Gaussian data and likelihood-based classifiers.