English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We address the problem of non-parametric density estimation under theadditional constraint that only privatised data are allowed to be published andavailable for inference. For this purpose, we adopt a recent generalisation ofclassical minimax theory to the framework of local $\alpha$-differentialprivacy and provide a lower bound on the rate of convergence over Besov spaces$B^s_{pq}$ under mean integrated $\mathbb L^r$-risk. This lower bound isdeteriorated compared to the standard setup without privacy, and reveals atwofold elbow effect. In order to fulfil the privacy requirement, we suggestadding suitably scaled Laplace noise to empirical wavelet coefficients. Upperbounds within (at most) a logarithmic factor are derived under the assumptionthat $\alpha$ stays bounded as $n$ increases: A linear but non-adaptive waveletestimator is shown to attain the lower bound whenever $p \geq r$ but provides aslower rate of convergence otherwise. An adaptive non-linear wavelet estimatorwith appropriately chosen smoothing parameters and thresholding is shown toattain the lower bound within a logarithmic factor for all cases.

Local differential privacy: Elbow effect in optimal density estimation and adaptation over Besov ellipsoids