Figure 3. Some examples where covariance does actually hurt the GNB's performance.

These were made by shifting the class centers, such that their perpendicular bisector is no longer parallel to the direction of maximal covariance. The regions of black crosses show where the covariance-ignoring GNB (green line) and the covariance-modeling LDA (purple line) yield different predictions. Nonetheless, these regions still form a relatively small proportion of the overall input space.