  Modern society depends on the flow of information over online social
networks, and users of popular platforms generate significant behavioral data
about themselves and their social ties. However, it remains unclear what
fundamental limits exist when using these data to predict the activities and
interests of individuals, and to what accuracy such predictions can be made
using an individual's social ties. Here we show that 95% of the potential
predictive accuracy for an individual is achievable using their social ties
only, without requiring that individual's data. We use information theoretic
tools to estimate the predictive information within the writings of Twitter
users, providing an upper bound on the available predictive information that
holds for any predictive or machine learning methods. As few as 8-9 of an
individual's contacts are sufficient to obtain predictability comparable to
that of the individual alone. Distinct temporal and social effects are visible
by measuring information flow along social ties, allowing us to better study
the dynamics of online activity. Our results have distinct privacy
implications: information is so strongly embedded in a social network that in
principle one can profile an individual from their available social ties even
when the individual forgoes the platform completely.
