Reviews: On Separability of Loss Functions, and Revisiting Discriminative Vs Generative Models

This paper starts by developing a notion of local "separability" of a loss function, which they use to get l_infty convertence rates, in terms of the separability parameters, for low and high dimensional settings. These rates are then applied to then applied to a probabilistic classification problem with both a generative and discriminative approach. After computing the teh separability parameters for each, they can apply the theorems to get l_infty convergence rates for the discriminative approach (logistic regression), as well as two generative approaches (for the cases that x y is isotropic Gaussian and gaussian graphical model). They next consider l_2 convergence rates. The discriminative rate is trivial based on the support consistency and the l_infty rates.