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Towards multi-purpose locally differentially-private synthetic data release via spline wavelet plug-in estimation
Thibault Randrianarisoa, Lukas Steinberger, Botond Szabó
We develop plug-in estimators for locally differentially private semi-parametric estimation via spline wavelets. The approach leads to optimal rates of convergence for a large clas…
Deep Horseshoe Gaussian Processes
Ismaël Castillo, Thibault Randrianarisoa
Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as…
Variational Gaussian Processes For Linear Inverse Problems
Thibault Randrianarisoa, Botond Szabo
By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an imag…
Optional Pólya trees: posterior rates and uncertainty quantification
Ismaël Castillo, Thibault Randrianarisoa
We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional Pólya trees as prior distribution. We derive near-optimal conv…