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Sparse Signal Detection in Heteroscedastic Gaussian Sequence Models: Sharp Minimax Rates
Given a heterogeneous Gaussian sequence model with unknown mean $\theta \in \mathbb R^d$ and known covariance matrix $\Sigma = \operatorname{diag}(\sigma_1^2,\dots, \sigma_d^2)$, we study the signal detection problem against sparse alternatives, for known sparsity $s$.
Benign overfitting and adaptive nonparametric regression
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older classes adaptively to the unknown smoothness.
Robust Estimation of Discrete Distributions under Local Differential Privacy
We consider the problem of estimating a discrete distribution in total variation from $n$ contaminated data batches under a local differential privacy constraint.
