# Variable coarsening in Naive Bayes

Say we have a binary classification problem that we solve with Naive Bayes. All features are categorical variables.

Say we focus on a single feature that takes one of $N$ possible values. If $N$ is high, and we use a discrete distribution to encode it, the model complexity can rapidly increase (one $\theta$ per value and feature).

One way of reducing model complexity (and potentially improve generalization performance if $N$ is relatively high) would be to cluster values of each variable and effectively use a smaller dictionary, reducing the number of $\theta$'s estimated. This would coarsen the probability mass function of every feature (variable) but since we end up with less parameters to estimate, it could help improve generalization performance.

Aside from cross-validation, what would be a principled way (good proxy) for identifying what values to group for a given variable/feature?