Robust and differentially private mean estimation
In statistical learning and analysis from shared data, which is increasingly widely adopted in
platforms such as federated learning and meta-learning, there are two major concerns …
platforms such as federated learning and meta-learning, there are two major concerns …
Covariance-aware private mean estimation without private covariance estimation
We present two sample-efficient differentially private mean estimators for $ d $-dimensional
(sub) Gaussian distributions with unknown covariance. Informally, given $ n\gtrsim d/\alpha …
(sub) Gaussian distributions with unknown covariance. Informally, given $ n\gtrsim d/\alpha …
Choosing among notions of multivariate depth statistics
K Mosler, P Mozharovskyi - Statistical Science, 2022 - projecteuclid.org
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis
distance from the mean, which is based on the mean and the covariance matrix of the data …
distance from the mean, which is based on the mean and the covariance matrix of the data …
A pseudo-metric between probability distributions based on depth-trimmed regions
The design of a metric between probability distributions is a longstanding problem motivated
by numerous applications in Machine Learning. Focusing on continuous probability …
by numerous applications in Machine Learning. Focusing on continuous probability …
Calibrated multiple-output quantile regression with representation learning
We develop a method to generate predictive regions that cover a multivariate response
variable with a user-specified probability. Our work is composed of two components. First …
variable with a user-specified probability. Our work is composed of two components. First …
Statistical depth functions for ranking distributions: definitions, statistical learning and applications
M Goibert, S Clémençon, E Irurozki… - arXiv preprint arXiv …, 2022 - arxiv.org
The concept of median/consensus has been widely investigated in order to provide a
statistical summary of ranking data, ie realizations of a random permutation $\Sigma $ of a …
statistical summary of ranking data, ie realizations of a random permutation $\Sigma $ of a …
Affine-invariant integrated rank-weighted depth: Definition, properties and finite sample analysis
G Staerman, P Mozharovskyi, S Clémençon - arXiv preprint arXiv …, 2021 - arxiv.org
Because it determines a center-outward ordering of observations in $\mathbb {R}^ d $ with $
d\geq 2$, the concept of statistical depth permits to define quantiles and ranks for …
d\geq 2$, the concept of statistical depth permits to define quantiles and ranks for …
Affine invariant integrated rank-weighted statistical depth: properties and finite sample analysis
S Clémençon, P Mozharovskyi… - Electronic Journal of …, 2023 - projecteuclid.org
Because it determines a center-outward ordering of observations in R d with d≥ 2, the
concept of statistical depth permits to define quantiles and ranks for multivariate data and …
concept of statistical depth permits to define quantiles and ranks for multivariate data and …
Another look at halfspace depth: flag halfspaces with applications
The halfspace depth is a well-studied tool of nonparametric statistics in multivariate spaces.
We introduce a flag halfspace–an intermediary between a closed halfspace and its interior …
We introduce a flag halfspace–an intermediary between a closed halfspace and its interior …
How to find a point in the convex hull privately
We study the question of how to compute a point in the convex hull of an input set $ S $ of $
n $ points in ${\mathbb R}^ d $ in a differentially private manner. This question, which is …
n $ points in ${\mathbb R}^ d $ in a differentially private manner. This question, which is …