  In our data world, a host of not necessarily trusted controllers gather data
on individual subjects. To preserve her privacy and, more generally, her
informational self-determination, the individual has to be empowered by giving
her agency on her own data. Maximum agency is afforded by local anonymization,
that allows each individual to anonymize her own data before handing them to
the data controller. Randomized response (RR) is a local anonymization approach
able to yield multi-dimensional full sets of anonymized microdata that are
valid for exploratory analysis and machine learning. This is so because an
unbiased estimate of the distribution of the true data of individuals can be
obtained from their pooled randomized data. Furthermore, RR offers rigorous
privacy guarantees. The main weakness of RR is the curse of dimensionality when
applied to several attributes: as the number of attributes grows, the accuracy
of the estimated true data distribution quickly degrades. We propose several
complementary approaches to mitigate the dimensionality problem. First, we
present two basic protocols, separate RR on each attribute and joint RR for all
attributes, and discuss their limitations. Then we introduce an algorithm to
form clusters of attributes so that attributes in different clusters can be
viewed as independent and joint RR can be performed within each cluster. After
that, we introduce an adjustment algorithm for the randomized data set that
repairs some of the accuracy loss due to assuming independence between
attributes when using RR separately on each attribute or due to assuming
independence between clusters in cluster-wise RR. We also present empirical
work to illustrate the proposed methods.
