Win-Vector LLC‘s Nina Zumel wrote a great article explaining differential privacy and demonstrating how to use it to enhance forward step-wise logistic regression (essentially reusing test data). This allowed her to reproduce results similar to the recent Science paper “The reusable holdout: Preserving validity in adaptive data analysis”. The technique essentially protects and reuses test data, allowing the series of adaptive decisions driving forward step-wise logistic regression to remain valid with respect to unseen future data. Without the differential privacy precaution these steps are not always sufficiently independent of each other to ensure good model generalization performance. Through differential privacy one gets safe reuse of test data across many adaptive queries, yielding more accurate estimates of out of sample performance, more robust choices, and resulting in a better model.
In this note I will discuss a specific related application: using differential privacy to reuse training data (or equivalently make training procedures more statistically efficient). I will also demonstrate similar effects using more familiar statistical techniques.