Round Blobs vs Squished Blobs

Two Gaussian generative models assume zero correlation between features. Model A uses covariance Σ=σ2I\Sigma = \sigma^2 I (one shared variance for all features). Model B uses covariance Σ=diag⁡(σ12,…,σd2)\Sigma = \operatorname{diag}(\sigma_1^2, \ldots, \sigma_d^2), allowing each feature its own variance. Which model's class-conditional density contours are always perfectly circular (spherical) in feature space?

A

Neither model can produce circular contours

B

Model A, the spherical Gaussian

C

Model B, the diagonal Gaussian

D

Both models produce circular contours