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Continual Mean Estimation Under User-Level Privacy
We provide an algorithm that outputs a mean estimate at every time instant $t$ such that the overall release is user-level $\varepsilon$-DP and has the following error guarantee: Denoting by $M_t$ the maximum number of samples contributed by a user, as long as $\tilde{\Omega}(1/\varepsilon)$ users have $M_t/2$ samples each, the error at time $t$ is $\tilde{O}(1/\sqrt{t}+\sqrt{M}_t/t\varepsilon)$.
Robust Testing in High-Dimensional Sparse Models
Our results show that the complexity of testing in these two settings significantly increases under robustness constraints.
An MCMC Method to Sample from Lattice Distributions
To generate samples from $P_\Lambda$, it suffices to draw samples from a pull-back measure $P_{\mathbb{Z}^d}$ defined on the integer lattice.
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