Minimax Supervised Clustering in the Anisotropic Gaussian Mixture Model: A new take on Robust Interpolation

Understand

We study the supervised clustering problem under the two-component anisotropic Gaussian mixture model in high dimensions and in the non-asymptotic setting.

• We first derive a lower and a matching upper bound for the minimax risk of clustering in this framework.
• We also show that in the high-dimensional regime, the linear discriminant analysis (LDA) classifier turns out to be sub-optimal in the minimax sense.
• Next, we characterize precisely the risk of $\ell_2$-regularized supervised least squares classifiers.