DP-GD achieves minimax optimal non-asymptotic risk O(γ + γ²/ρ²) for well-conditioned high-dimensional data and power-law scaling for ill-conditioned power-law spectra, with the exponent depending on the privacy parameter ρ.
We, therefore, have that∥ 1 n2 ⟨b⊗2 k −I d, Ck⟩∥ψ1 ≤Cn −1, for some constantC(ρ, c, C η, 1)>0
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High-Dimensional Private Linear Regression with Optimal Rates
DP-GD achieves minimax optimal non-asymptotic risk O(γ + γ²/ρ²) for well-conditioned high-dimensional data and power-law scaling for ill-conditioned power-law spectra, with the exponent depending on the privacy parameter ρ.