Related papers: Robust Testing in High-Dimensional Sparse Models
We consider inference in linear regression models that is robust to heteroskedasticity and the presence of many control variables. When the number of control variables increases at the same rate as the sample size the usual…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
This paper studies the problem of accurately recovering a sparse vector $\beta^{\star}$ from highly corrupted linear measurements $y = X \beta^{\star} + e^{\star} + w$ where $e^{\star}$ is a sparse error vector whose nonzero entries may be…
Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…
We study the problem of recovering an $s$-sparse signal $\mathbf{x}^{\star}\in\mathbb{C}^n$ from corrupted measurements $\mathbf{y} = \mathbf{A}\mathbf{x}^{\star}+\mathbf{z}^{\star}+\mathbf{w}$, where $\mathbf{z}^{\star}\in\mathbb{C}^m$ is…
We consider the change point testing problem for high-dimensional time series. Unlike conventional approaches, where one tests whether the difference $\delta$ of the mean vectors before and after the change point is equal to zero, we argue…
In the high-dimensional sparse modeling literature, it has been crucially assumed that the sparsity structure of the model is homogeneous over the entire population. That is, the identities of important regressors are invariant across the…
Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…
We study estimation of an $s$-sparse signal in the $p$-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely the rate scales with respect to…
We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…
This paper explores the validity of the two-stage estimation procedure for sparse linear models in high-dimensional settings with possibly many endogenous regressors. In particular, the number of endogenous regressors in the main equation…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
We give nearly optimal bounds on the sample complexity of $(\widetilde{\Omega}(\epsilon),\epsilon)$-tolerant testing the $\rho$-independent set property in the dense graph setting. In particular, we give an algorithm that inspects a random…
We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…
We study robust high-dimensional sparse regression under finite-variance heavy-tailed noise, epsilon-contamination, and alpha-mixing dependence via two subsampling estimators: Adaptive Importance Sampling (AIS) and Stratified Sub-sampling…
The problem of consistently estimating the sparsity pattern of a vector $\betastar \in \real^\mdim$ based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…