We consider statistical models which have been proposed for luminosity distributions for the globular clusters in the Milky Way and M31. Although earlier research showed that the cluster luminosity functions in those two galaxies were well fit by Gaussian distributions, subsequent investigations suggested that their luminosities were better fit by t-, rather than Gaussian, distributions. By app...

We give the first representation-independent hardness result for agnostically learning halfspaces with respect to the Gaussian distribution. We reduce from the problem of learning sparse parities with noise with respect to the uniform distribution on the hypercube (sparse LPN), a notoriously hard problem in theoretical computer science and show that any algorithm for agnostically learning halfs...