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This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…

Systems and Control · Computer Science 2018-07-27 Chiara Ravazzi , Nelson P. K. Chan , Paolo Frasca

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus…

Statistics Theory · Mathematics 2019-06-12 Gabor Lugosi , Shahar Mendelson

Recent algebraic parametric estimation techniques led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal. In this paper, we extend such differentiation methods by providing a larger choice…

Numerical Analysis · Mathematics 2011-03-04 Da-Yan Liu , Olivier Gibaru , Wilfrid Perruquetti

There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training…

Machine Learning · Statistics 2025-10-30 Fabian Schaipp , Guillaume Garrigos , Umut Simsekli , Robert Gower

The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns…

Systems and Control · Electrical Eng. & Systems 2023-06-19 Jean-Sébastien Brouillon , Florian Dörfler , Giancarlo Ferrari-Trecate

We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal…

Statistics Theory · Mathematics 2020-02-25 Gabor Lugosi , Shahar Mendelson

Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…

Machine Learning · Computer Science 2022-12-21 Jongheon Jeong , Seojin Kim , Jinwoo Shin

As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…

Statistics Theory · Mathematics 2024-09-12 Li Tuobang

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…

Computation · Statistics 2019-05-29 Stefano Peluso , Antonietta Mira , Pietro Muliere

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…

Discrete Mathematics · Computer Science 2018-03-14 Kevin Buchin , Jeff M. Phillips , Pingfan Tang

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…

Machine Learning · Statistics 2025-12-12 Gabriel Clara , Yazan Mash'al

We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that…

Statistics Theory · Mathematics 2017-02-03 Gábor Lugosi , Shahar Mendelson

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…

Statistics Theory · Mathematics 2013-11-05 Xinjia Chen

In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…

Machine Learning · Statistics 2017-03-01 Jun Han , Qiang Liu

This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…

Signal Processing · Electrical Eng. & Systems 2018-05-03 Paolo Carbone , Johan Schoukens , István Kollár , Antonio Moschitta

The paper proposes some robust estimators of the finite population mean. Such estimators are particularly suitable in the presence of some outlying observations. Included as special cases of our general result are robust versions of the…

Statistics Theory · Mathematics 2008-12-18 Malay Ghosh

In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…

Information Theory · Computer Science 2020-01-23 Michael Fauß , Abdelhak M. Zoubir , Alex Dytso , H. Vincent Poor , K. G. Nagananda

We consider the problem of estimating the mean and covariance of a distribution from iid samples in $\mathbb{R}^n$, in the presence of an $\eta$ fraction of malicious noise; this is in contrast to much recent work where the noise itself is…

Data Structures and Algorithms · Computer Science 2016-08-16 Kevin A. Lai , Anup B. Rao , Santosh Vempala

We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean…

Data Structures and Algorithms · Computer Science 2022-11-30 Ilias Diakonikolas , Daniel M. Kane , Jasper C. H. Lee , Ankit Pensia

It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…

Statistics Theory · Mathematics 2025-12-03 Roberto I. Oliveira , Lucas Resende