相关论文: Efficient Robust Constrained Signal Detection via …

We study the optimality of the minimax risk of truncated series estimators for symmetric convex polytopes. We show that the optimal truncated series estimator is within $O(\log m)$ factor of the optimal if the polytope is defined by $m$…

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…

This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge…

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…

Compressed sensing seeks to invert an underdetermined linear system by exploiting additional knowledge of the true solution. Over the last decade, several instances of compressed sensing have been studied for various applications, and for…

Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…

In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

We consider a matrix-valued Gaussian sequence model, that is, we observe a sequence of high-dimensional $M \times N$ matrices of heterogeneous Gaussian random variables $x_{ij,k}$ for $i \in\{1,...,M\}$, $j \in \{1,...,N\}$ and $k \in…

This paper investigates model reduction methods for efficiently approximating the solution of parameter-dependent PDEs with a multi-parameter vector $\vec{\mu} \in \mathbb{R}^p$. In cases where the Kolmogorov $N$-width decays fast enough,…

This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis…

We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among…

We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…

A new robust algorithm based of the explanation method SurvLIME called SurvLIME-KS is proposed for explaining machine learning survival models. The algorithm is developed to ensure robustness to cases of a small amount of training data or…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…