Related papers: Model Selection for High-Dimensional Regression un…

We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear…

We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…

We consider the high-dimensional linear regression model $Y = X \beta^0 + \epsilon$ with Gaussian noise $\epsilon$ and Gaussian random design $X$. We assume that $\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\Theta :=…

The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…

Feature selection and importance estimation in a model-agnostic setting is an ongoing challenge of significant interest. Wrapper methods are commonly used because they are typically model-agnostic, even though they are computationally…

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…

We introduce and study the Group Square-Root Lasso (GSRL) method for estimation in high dimensional sparse regression models with group structure. The new estimator minimizes the square root of the residual sum of squares plus a penalty…

We consider the problem of simultaneous variable selection and constant coefficient identification in high-dimensional varying coefficient models based on B-spline basis expansion. Both objectives can be considered as some type of model…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Group-Lasso (gLasso) identifies important explanatory factors in predicting the response variable by considering the grouping structure over input variables. However, most existing algorithms for gLasso are not scalable to deal with…

In linear models it is common to have situations where several regression coefficients are zero. In these situations a common tool to perform regression is a variable selection operator. One of the most common such operators is the LASSO…

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research…

In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed…

Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

In this paper, we study the problem of signal estimation from noisy non-linear measurements when the unknown $n$-dimensional signal is in the range of an $L$-Lipschitz continuous generative model with bounded $k$-dimensional inputs. We make…

This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…

This paper considers generalized least squares (GLS) estimation for linear panel data models. By estimating the large error covariance matrix consistently, the proposed feasible GLS (FGLS) estimator is more efficient than the ordinary least…