Data selection improves privacy aware transfer learning performance
High-Dimensional Asymptotics and Dataset Selection for Private Transfer Learning
Machine Learning
Summary
Deciding whether to use extra data from others can be hard when you can only see summary information and want to keep data private. The authors propose a new math framework that predicts if adding private data will help or hurt learning, accounting for differences in data and noise added for privacy. Their method estimates how well a model will do using overall data statistics, without needing the full data itself. This helps choose wisely about buying or sharing sensitive data with privacy guarantees.
What this means in practice
- •For machine learning engineers: Improve model accuracy decisions when incorporating external private datasets using only summary statistics without accessing raw data.
- •For data privacy officers: Assess the trade-offs between privacy noise and data utility for transfer learning in collaborative or purchased data settings.
Authors
Filip Kovačević, Edwige Cyffers, Stefano Sarao Mannelli, Marco Mondelli
Abstract
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 (weights and ridge regularizers) and, more broadly, to decide when private external datasets are useful without accessing the data itself but only relying on population-level quantities. This provides a theoretically tractable foundation for private transfer learning, which we support via experiments on both synthetic and real-world datasets.