Related papers: Sample Complexity Bounds for Robust Mean Estimatio…
Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…
The setting of a right-censored random sample subject to contamination is considered. In various fields, expert information is often available and used to overcome the contamination. This paper integrates expert knowledge into the…
We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…
High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting…
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…
Accurate estimates of microbial species abundances are needed to advance our understanding of the role that microbiomes play in human and environmental health. However, artificially constructed microbiomes demonstrate that intuitive…
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…
Algorithmic robust statistics has traditionally focused on the contamination model where a small fraction of the samples are arbitrarily corrupted. We consider a recent contamination model that combines two kinds of corruptions: (i) small…
This paper studies a structural failure of subsample-based estimation in dynamic time series models. Even under oracle knowledge of contamination locations, removing contaminated observations does not restore the uncontaminated objective.…
In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
In contrast to the empirical mean, the Median-of-Means (MoM) is an estimator of the mean $\theta$ of a square integrable r.v. $Z$, around which accurate nonasymptotic confidence bounds can be built, even when $Z$ does not exhibit a…
The radiological characterization of contaminated elements (walls, grounds, objects) from nuclear facilities often suffers from a too small number of measurements. In order to determine risk prediction bounds on the level of contamination,…
We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…
We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…
The Fourier Basis Density Model (FBM) was recently introduced as a flexible probability model for band-limited distributions, i.e. ones which are smooth in the sense of having a characteristic function with limited support around the…