  We consider the problem of assigning weights to a set of samples or data
records, with the goal of achieving a representative weighting, which happens
when certain sample averages of the data are close to prescribed values. We
frame the problem of finding representative sample weights as an optimization
problem, which in many cases is convex and can be efficiently solved. Our
formulation includes as a special case the selection of a fixed number of the
samples, with equal weights, i.e., the problem of selecting a smaller
representative subset of the samples. While this problem is combinatorial and
not convex, heuristic methods based on convex optimization seem to perform very
well. We describe rsw, an open-source implementation of the ideas described in
this paper, and apply it to a skewed sample of the CDC BRFSS dataset.
