相关论文: Non-Asymptotic Guarantees for Reliable Identificat…

Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…

We show, using three empirical applications, that linear regression estimates predicated on the assumption of sparsity are fragile in two ways. First, we document that different choices of the regressor matrix which do not impact ordinary…

Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering…

Linear Vector AutoRegressive (VAR) models where the innovations could be unconditionally heteroscedastic and serially dependent are considered. The volatility structure is deterministic and quite general, including breaks or trending…

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…

One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained $\ell_1$-minimization. The majority of initial works focused on real (sub-)Gaussian…

Causal graph discovery is a significant problem with applications across various disciplines. However, with observational data alone, the underlying causal graph can only be recovered up to its Markov equivalence class, and further…

The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to…

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Real-time monitoring in modern medical research introduces functional longitudinal data, characterized by continuous-time measurements of outcomes, treatments, and confounders. This complexity leads to uncountably infinite…

Causal discovery between collections of time-series data can help diagnose causes of symptoms and hopefully prevent faults before they occur. However, reliable causal discovery can be very challenging, especially when the data acquisition…

\textbf{Background:} Mediation analysis is widely used to investigate how treatments and programs exert their effects, but standard ordinary least squares (OLS) inference can be unreliable when regression errors are non-Gaussian. In medical…

Quantifying uncertainty in high-dimensional sparse linear regression is a fundamental task in statistics that arises in various applications. One of the most successful methods for quantifying uncertainty is the debiased LASSO, which has a…

We present a new methodology for simultaneous variable selection and parameter estimation in function-on-scalar regression with an ultra-high dimensional predictor vector. We extend the LASSO to functional data in both the $\textit{dense}$…

The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…

To unbiasedly estimate a causal effect on an outcome unconfoundedness is often assumed. If there is sufficient knowledge on the underlying causal structure then existing confounder selection criteria can be used to select subsets of the…

Causal inference in multivariate time series is challenging due to the fact that the sampling rate may not be as fast as the timescale of the causal interactions. In this context, we can view our observed series as a subsampled version of…

The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…

Panel data are widely used in political science to draw causal inferences. However, these models often rely on the strong and untested assumption of sequential ignorability--that no unmeasured variables influence both the independent and…