  Many data sources are naturally modeled by multiple weight assignments over a
set of keys: snapshots of an evolving database at multiple points in time,
measurements collected over multiple time periods, requests for resources
served at multiple locations, and records with multiple numeric attributes.
Over such vector-weighted data we are interested in aggregates with respect to
one set of weights, such as weighted sums, and aggregates over multiple sets of
weights such as the $L_1$ difference.
  Sample-based summarization is highly effective for data sets that are too
large to be stored or manipulated. The summary facilitates approximate
processing queries that may be specified after the summary was generated.
  Current designs, however, are geared for data sets where a single {\em
scalar} weight is associated with each key.
  We develop a sampling framework based on {\em coordinated weighted samples}
that is suited for multiple weight assignments and obtain estimators that are
{\em orders of magnitude tighter} than previously possible.
  We demonstrate the power of our methods through an extensive empirical
evaluation on diverse data sets ranging from IP network to stock quotes data.
