no code implementations • 2 Dec 2022 • Cristina Butucea, Jean-François Delmas, Anne Dutfoy, Clément Hardy
It turns out that, in this framework, our upper bound on the minimax separation rate matches (up to a logarithmic factor) the lower bound on the minimax separation rate for signal detection in the high dimensional linear model associated to a fixed dictionary of features.
no code implementations • 27 Oct 2022 • Cristina Butucea, Jean-François Delmas, Anne Dutfoy, Clément Hardy
Following recent works on the geometry of off-the-grid methods, we show that such functions can be constructed provided the parameters of the active features are pairwise separated by a constant with respect to a Riemannian metric. When the number of signals is finite and the noise is assumed Gaussian, we give refinements of our results for $p=1$ and $p=2$ using tail bounds on suprema of Gaussian and $\chi^2$ random processes.
no code implementations • 29 Jun 2022 • Cristina Butucea, Jean-François Delmas, Anne Dutfoy, Clément Hardy
We propose an off-the-grid optimization method, that is, a method which does not use any discretization scheme on the parameter space, to estimate both the non-linear parameters of the features and the linear parameters of the mixture.
no code implementations • NeurIPS 2021 • Cristina Butucea, Yann Issartel
In the non-interactive case, we study two plug-in type estimators of $F_{\gamma}$, for all $\gamma >0$, that are similar to the MLE analyzed by Jiao et al. (2017) in the multinomial model.
no code implementations • NeurIPS 2021 • Cristina Butucea, Yann Issartel
In the non-interactive case, we study several plug-in type estimators of $F_{\gamma}$, for all $\gamma >0$, that are similar to the MLE which has been analyzed by Jiao et al. (2017) in the multinomial model.
no code implementations • NeurIPS 2020 • Thomas B. Berrett, Cristina Butucea
We construct efficient randomized algorithms and test procedures, in both the case where only non-interactive privacy mechanisms are allowed and also in the case where all sequentially interactive privacy mechanisms are allowed.
no code implementations • 10 Dec 2019 • Thomas Berrett, Cristina Butucea
We consider the binary classification problem in a setup that preserves the privacy of the original sample.