  Users of a personalised recommendation system face a dilemma: recommendations
can be improved by learning from data, but only if the other users are willing
to share their private information. Good personalised predictions are vitally
important in precision medicine, but genomic information on which the
predictions are based is also particularly sensitive, as it directly identifies
the patients and hence cannot easily be anonymised. Differential privacy has
emerged as a potentially promising solution: privacy is considered sufficient
if presence of individual patients cannot be distinguished. However,
differentially private learning with current methods does not improve
predictions with feasible data sizes and dimensionalities. Here we show that
useful predictors can be learned under powerful differential privacy
guarantees, and even from moderately-sized data sets, by demonstrating
significant improvements with a new robust private regression method in the
accuracy of private drug sensitivity prediction. The method combines two key
properties not present even in recent proposals, which can be generalised to
other predictors: we prove it is asymptotically consistently and efficiently
private, and demonstrate that it performs well on finite data. Good finite data
performance is achieved by limiting the sharing of private information by
decreasing the dimensionality and by projecting outliers to fit tighter bounds,
therefore needing to add less noise for equal privacy. As already the
simple-to-implement method shows promise on the challenging genomic data, we
anticipate rapid progress towards practical applications in many fields, such
as mobile sensing and social media, in addition to the badly needed precision
medicine solutions.
