Differentially Private Learning Beyond the Classical Dimensionality Regime

Cynthia Dwork, Pranay Tankala, Linjun Zhang

Abstract: We initiate the study of differentially private learning in the proportional dimensionality regime, in which the number of data samples n and problem dimension d approach infinity at rates proportional to one another, meaning that \(d / n \rightarrow \delta \) as \(n \rightarrow \infty \) for an arbitrary, given constant \(\delta \in (0, \infty )\). This setting is significantly more challenging than that of all prior theoretical work in high-dimensional differentially private learning, which, despite the name, has assumed that \(\delta = 0\) or is sufficiently small for problems of sample complexity O(d), a regime typically considered “low-dimensional” or “classical” by modern standards in high-dimensional statistics.

External IDs:doi:10.1007/978-3-032-12290-2_11