  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.
