9 problems

The elements of a configuration are points in the $(m-1)$-dimensional probability simplex in $\mathbb{R}^m$. A configuration is extremal if it arises as the configuration associate…

Averaged TV-risk conjecture. The upper bound above may not be tight; it is an open problem whether it can be improved to

Laplace-privatization rate conjecture. On the basis of data privatized in this way, the same rates of convergence as those derived below should be attainable.

Slow-rate conjecture. If the SDA is not fulfilled, the rate of convergence can be arbitrarily slow.

Compact-support conjecture. The condition that the density function of interest is supported on a compact set is critical for achieving optimality under both contamination and loca…

Let $X_i$ denote the data vector observed by the $i$-th data-holder. A privacy mechanism is interactive when the randomization of $X_i$ may use publicly available information from…

Let $\mathcal P$ be the model class, let $\theta$ be a linear functional on distributions in $\mathcal P$, and suppose observations are subject to local differential privacy. The r…

Let $n\in\mathbb{N}$ be the sample size, let $\alpha>0$ be the privacy parameter, and let $\omega_{TV}$ and $\omega_H$ denote the total-variation and Hellinger moduli appearing in…

Let $\mathcal{D}$ be the local differential privacy polytope, let $\operatorname{ex}(\mathcal{D})$ denote its set of extreme points, and let $\tilde{\mathcal{D}}'$ and…