High-Dimensional Asymptotics and Dataset Selection for Private Transfer Learning

Filip Kovačević, Edwige Cyffers, Stefano Sarao Mannelli, Marco Mondelli

To commit to buying external data or participate in collaborative learning, one must decide whether the additional data will improve prediction enough to justify the cost. This comes with several challenges: (i) the decision often relies only on aggregated statistics available publicly, rather than individual-level data; (ii) covariate and model shifts can induce negative transfer, so the additional data deteriorates rather than improves performance; (iii) if the data is sensitive, its privatization requires the injection of noise, which can also offset the benefit of a larger sample size. In this paper, we model the problem of dataset selection through high-dimensional regression with multiple heterogeneous sources and a weighted ridge estimator. Our approach uses only summary statistics and it gives privacy guarantees either on labels only or jointly on features and labels, in terms of $ρ$-zero-concentrated differential privacy. The main technical contribution is a deterministic equivalent of the test error, which captures the interactions between sample size, covariance structure, model shift, regularization and privacy noise. Our theory allows to optimize hyperparameters…