  Differential privacy is often applied with a privacy parameter that is larger
than the theory suggests is ideal; various informal justifications for
tolerating large privacy parameters have been proposed. In this work, we
consider partial differential privacy (DP), which allows quantifying the
privacy guarantee on a per-attribute basis. In this framework, we study several
basic data analysis and learning tasks, and design algorithms whose
per-attribute privacy parameter is smaller that the best possible privacy
parameter for the entire record of a person (i.e., all the attributes).
