17 citations · 43 across the 12 of their papers we have counts for
13 papers
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…
Implicit vs. explicit regularization for high-dimensional gradient descent
Thomas Stark, Lukas Steinberger
In this paper we investigate the generalization error of gradient descent (GD) applied to an -regularized OLS objective function in the linear model. Based on our analysis…
Efficient Estimation of a Gaussian Mean with Local Differential Privacy
Nikita P. Kalinin, Lukas Steinberger
In this paper we study the problem of estimating the unknown mean of a unit variance Gaussian distribution in a locally differentially private (LDP) way. In the high-privacy re…
Uncertainty quantification via cross-validation and its variants under algorithmic stability
Nicolai Amann, Hannes Leeb, Lukas Steinberger
Recently, there has been substantial interest in statistical guarantees for cross-validation (CV) methods of uncertainty quantification in statistical learning (cf. Barber et al. 2…
Efficiency in local differential privacy
Lukas Steinberger
We develop a theory of asymptotic efficiency in regular parametric models when data confidentiality is ensured by local differential privacy (LDP). Even though efficient parameter…
Interactive versus non-interactive locally differentially private estimation: Two elbows for the quadratic functional
Cristina Butucea, Angelika Rohde, Lukas Steinberger
Local differential privacy has recently received increasing attention from the statistics community as a valuable tool to protect the privacy of individual data owners without the…
Statistical inference with F-statistics when fitting simple models to high-dimensional data
Hannes Leeb, Lukas Steinberger
We study linear subset regression in the context of the high-dimensional overall model with univariate response and a -vector of random regressors $…
Conditional predictive inference for stable algorithms
Lukas Steinberger, Hannes Leeb
We investigate generically applicable and intuitively appealing prediction intervals based on -fold cross validation. We focus on the conditional coverage probability of the pro…
Geometrizing rates of convergence under local differential privacy constraints
Angelika Rohde, Lukas Steinberger
We study the problem of estimating a functional of an unknown probability distribution in which the original iid sample is…
Uniformly valid confidence intervals post-model-selection
François Bachoc, David Preinerstorfer, Lukas Steinberger
We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Ber…
Leave-one-out prediction intervals in linear regression models with many variables
Lukas Steinberger, Hannes Leeb
We study prediction intervals based on leave-one-out residuals in a linear regression model where the number of explanatory variables can be large compared to sample size. We estab…
The relative effects of dimensionality and multiplicity of hypotheses on the F-test in linear regression
Lukas Steinberger
Recently, several authors have re-examined the power of the classical F-test in linear regression in a `large-p, large-n' framework (cf. Zhong and Chen (2011), Wang and Cui (2013))…
On conditional moments of high-dimensional random vectors given lower-dimensional projections
Lukas Steinberger, Hannes Leeb
One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional vari…