Related papers: When does the Tukey median work?

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…

In this paper, we establish error estimates for a fully discrete, filtered Lie splitting scheme applied directly to the Zakharov system -- a model whose solutions may exhibit extremely low regularity in arbitrary dimensions. Remarkably, we…

We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements…

We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…

Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…

We establish the pointwise convergence of the iterative Lloyd algorithm, also known as $k$-means algorithm, when the quadratic quantization error of the starting grid (with size $N\ge 2$) is lower than the minimal quantization error with…

The Tucker decomposition generalizes the notion of Singular Value Decomposition (SVD) to tensors, the higher dimensional analogues of matrices. We study the problem of constructing the Tucker decomposition of sparse tensors on distributed…

With the proliferation of generative AI and the increasing volume of generative data (also called as synthetic data), assessing the fidelity of generative data has become a critical concern. In this paper, we propose a discriminative…

The current best approximation algorithms for $k$-median rely on first obtaining a structured fractional solution known as a bi-point solution, and then rounding it to an integer solution. We improve this second step by unifying and…

We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…

Conformal prediction is a non-parametric technique for constructing prediction intervals or sets from arbitrary predictive models under the assumption that the data is exchangeable. It is popular as it comes with theoretical guarantees on…

Motivated by the widely used geometric median-of-means estimator in machine learning, this paper studies statistical inference for ultrahigh dimensionality location parameter based on the sample spatial median under a general multivariate…

We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets. The naive approach is to take the empirical mean of each…

One of the most basic problems in reinforcement learning (RL) is policy evaluation: estimating the long-term return, i.e., value function, corresponding to a given fixed policy. The celebrated Temporal Difference (TD) learning algorithm…

We compute the robustness of Fermat-Weber points with respect to any finite gauge. We show a breakdown point of $1/(1+\sigma)$ where $\sigma$ is the asymmetry measure of the gauge. We obtain quantitative results indicating how far a…

We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…

In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…

In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of…

Le Cam's two-point testing method yields perhaps the simplest lower bound for estimating the mean of a distribution: roughly, if it is impossible to well-distinguish a distribution centered at $\mu$ from the same distribution centered at…

Given i.i.d.~samples from an unknown distribution $P$, the goal of distribution learning is to recover the parameters of a distribution that is close to $P$. When $P$ belongs to the class of product distributions on the Boolean hypercube…