Related papers: Robust Sparse Regression with Non-Isotropic Design…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…

We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured…

We study active learning of homogeneous $s$-sparse halfspaces in $\mathbb{R}^d$ under the setting where the unlabeled data distribution is isotropic log-concave and each label is flipped with probability at most $\eta$ for a parameter $\eta…

The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant…

Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…

Vector autoregressive (VAR) models are widely used for causal discovery and forecasting in multivariate time series analysis. In the high-dimensional setting, which is increasingly common in fields such as neuroscience and econometrics,…

We study the learnability of linear separators in $\Re^d$ in the presence of bounded (a.k.a Massart) noise. This is a realistic generalization of the random classification noise model, where the adversary can flip each example $x$ with…

In the Wishart model for sparse PCA we are given $n$ samples $Y_1,\ldots, Y_n$ drawn independently from a $d$-dimensional Gaussian distribution $N({0, Id + \beta vv^\top})$, where $\beta > 0$ and $v\in \mathbb{R}^d$ is a $k$-sparse unit…

Recent results have proven the minimax optimality of LASSO and related algorithms for noisy linear regression. However, these results tend to rely on variance estimators that are inefficient or optimizations that are slower than LASSO…

We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…

We give a proof of the conjecture of Nelson and Nguyen [FOCS 2013] on the optimal dimension and sparsity of oblivious subspace embeddings, up to sub-polylogarithmic factors: For any $n\geq d$ and $\epsilon\geq d^{-O(1)}$, there is a random…

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…

This paper introduces a novel recursive distributed estimation algorithm aimed at synthesizing input and state interval observers for nonlinear bounded-error discrete-time multi-agent systems. The considered systems have sensors and…

Orthogonal matching pursuit (OMP) and orthogonal least squares (OLS) are widely used for sparse signal reconstruction in under-determined linear regression problems. The performance of these compressed sensing (CS) algorithms depends…

We tackle estimating sparse coefficients in a linear regression when the covariates are sampled from an $L$-subexponential random vector. This vector belongs to a class of distributions that exhibit heavier tails than Gaussian random…

Machine learning and artificial intelligence algorithms typically require large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden…

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

Dynamical systems can confront one of two extreme types of disturbances: persistent zero-mean independent noise, and sparse nonzero-mean adversarial attacks, depending on the specific scenario being modeled. While mean-based estimators like…

In this note, we analyze an iterative soft / hard thresholding algorithm with homotopy continuation for recovering a sparse signal $x^\dag$ from noisy data of a noise level $\epsilon$. Under suitable regularity and sparsity conditions, we…