Carnival of Samplings: Nets, Approximations, Relative and Sensitive

In this write-up, we are interested in how much information can be extracted by random sampling of a certain size for a range space of VC dimension d. In particular, we show that several standard results about samplings follow from the sampling theorem of Lin et al. [LLS01]. The following assumes that the reader is familiar and comfortable with ε-nets and εapproximations. The results surveyed in this write-up are summarized in Figure 1.