  Data mining information about people is becoming increasingly important in
the data-driven society of the 21st century. Unfortunately, sometimes there are
real-world considerations that conflict with the goals of data mining;
sometimes the privacy of the people being data mined needs to be considered.
This necessitates that the output of data mining algorithms be modified to
preserve privacy while simultaneously not ruining the predictive power of the
outputted model. Differential privacy is a strong, enforceable definition of
privacy that can be used in data mining algorithms, guaranteeing that nothing
will be learned about the people in the data that could not already be
discovered without their participation. In this survey, we focus on one
particular data mining algorithm -- decision trees -- and how differential
privacy interacts with each of the components that constitute decision tree
algorithms. We analyze both greedy and random decision trees, and the conflicts
that arise when trying to balance privacy requirements with the accuracy of the
model.
