Dimension-Free Private Mean Estimation is Impossible Without the Covariance
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2603. 19703v2 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications.
arXiv:2609. 22783v1 Announce Type: new Abstract: We study differentially private covariance estimation in operator norm for mean-zero sub-Gaussian distributions with unknown covariance support and at most $k$ nonzero entries per row.
The paper presents a Gaussian approximation for the privacy loss distribution in differentially private stochastic gradient descent (DP‑SGD) when subsampling is used. It shows that, after truncating rare large losses, the privacy loss behaves like a Gaussian with the same mean and variance, up to a small shift that grows only logarithmically with the error tolerance. This leads to tighter variance‑based bounds for subsampled mechanisms, improving upon previous Renyi‑divergence analyses and explaining the effectiveness of the connect‑the‑dots method for random allocation sampling.
arXiv:2610. 02716v1 Announce Type: new Abstract: Objective perturbation adds a random linear term to a regularized empirical risk and releases the exact perturbed minimizer.
arXiv:2504.00919v3 Announce Type: replace-cross Abstract: We study the problem of estimating the spectral density of a centered stationary Gaussian time series under local differential privacy constr...
We study learning a discrete distribution under person-level differential privacy in the batched setting. Given $n$ users, each contributing $m$ i.