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.
Homogenization of sgd in high- dimensions: exact dynamics and generalization properties.Mathematical Programming, 2024a
2 Pith papers cite this work, alongside 3 external citations. Polarity classification is still indexing.
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In the high-dimensional regime, SGD on diagonal linear networks is approximated by an SDE and a deterministic PDE that together give an explicit non-asymptotic description of convergence to zero risk.
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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.
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High-dimensional Limit of SGD for Diagonal Linear Networks
In the high-dimensional regime, SGD on diagonal linear networks is approximated by an SDE and a deterministic PDE that together give an explicit non-asymptotic description of convergence to zero risk.