Specifically,GSPENs combine thecapabilities ofclassicalstructured prediction models andSPENs andhavetheability toexplicitly model localstructure whenknown or assumed, while providing the ability to learn an unknown or more global structure implicitly.

In this work, we give a framework for improving the robustness of classifiers to adversaries with L0 noise budgets.

Entropy estimation is one of the prototypical problems in distribution property testing.

In this paper,we consider the learning problem where the projected data isfurther compressed byscalarquantization, which iscalled quantized compressivelearning. Generalization error bounds are derived for three models: nearest neighbor (NN) classifier, linear classifier and least squares regression.

Weprove its pointwise universality, i.e., it achieves a normalized log loss performance asymptotically as good as the true conditional entropy of the labels given the features.

After prediction, the true labelyt is revealed and the lossℓ(yt,ˆyt)is incurred.