Related papers: Lasso Inference for High-Dimensional Time Series
In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression…
This paper proposes a new method of inference in high-dimensional regression models and high-dimensional IV regression models. Estimation is based on a combined use of the orthogonal greedy algorithm, high-dimensional Akaike information…
Accurate gene regulatory networks can be used to explain the emergence of different phenotypes, disease mechanisms, and other biological functions. Many methods have been proposed to infer networks from gene expression data but have been…
There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on…
For high-dimensional omics data, sparsity-inducing regularization methods such as the Lasso are widely used and often yield strong predictive performance, even in settings when the assumption of sparsity is likely violated. We demonstrate…
We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge…
Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…
Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates…
In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first-…
Performing statistical inference in high-dimension is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional estimators. Here, we consider linear regression in…
Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected…
Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
High-dimensional regression models with regularized sparse estimation are widely applied. For statistical inferences, debiased methods are available about single coefficients or predictions with sparse new covariate vectors (also called…
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…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…
Classically, confidence intervals are required to have consistent coverage across all values of the parameter. However, this will inevitably break down if the underlying estimation procedure is biased. For this reason, many efforts have…
These lecture notes consist of three chapters. In the first chapter we present oracle inequalities for the prediction error of the Lasso and square-root Lasso and briefly describe the scaled Lasso. In the second chapter we establish…
We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is…