  Geographically annotated social media is extremely valuable for modern
information retrieval. However, when researchers can only access
publicly-visible data, one quickly finds that social media users rarely publish
location information. In this work, we provide a method which can geolocate the
overwhelming majority of active Twitter users, independent of their location
sharing preferences, using only publicly-visible Twitter data.
  Our method infers an unknown user's location by examining their friend's
locations. We frame the geotagging problem as an optimization over a social
network with a total variation-based objective and provide a scalable and
distributed algorithm for its solution. Furthermore, we show how a robust
estimate of the geographic dispersion of each user's ego network can be used as
a per-user accuracy measure which is effective at removing outlying errors.
  Leave-many-out evaluation shows that our method is able to infer location for
101,846,236 Twitter users at a median error of 6.38 km, allowing us to geotag
over 80\% of public tweets.
