Related papers: The Geometric Median and Applications to Robust Me…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
Online averaged stochastic gradient algorithms are more and more studied since (i) they can deal quickly with large sample taking values in high dimensional spaces, (ii) they enable to treat data sequentially, (iii) they are known to be…
In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…
We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…
We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional…
We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
Historically used in settings where the outcome is rare or data collection is expensive, outcome-dependent sampling is relevant to many modern settings where data is readily available for a biased sample of the target population, such as…
We study high-dimensional mean estimation in a collaborative setting where data is contributed by $N$ users in batches of size $n$. In this environment, a learner seeks to recover the mean $\mu$ of a true distribution $P$ from a collection…
A central part of geometric statistics is to compute the Fr\'echet mean. This is a well-known intrinsic mean on a Riemannian manifold that minimizes the sum of squared Riemannian distances from the mean point to all other data points. The…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
Most of the modern literature on robust mean estimation focuses on designing estimators which obtain optimal sub-Gaussian concentration bounds under minimal moment assumptions and sometimes also assuming contamination. This work looks at…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…