Related papers: Adaptive Estimation and Statistical Inference for …
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
We consider statistical inference for network-linked regression problems, where covariates may include network summary statistics computed for each node. In settings involving network data, it is often natural to posit that latent variables…
Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set keeps good statistical properties of the original estimator under standard assumptions, and guarantees valid average…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…
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…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
This paper considers the estimation and prediction of a high-dimensional linear regression in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related regression…
The fused lasso, also known as total-variation denoising, is a locally-adaptive function estimator over a regular grid of design points. In this paper, we extend the fused lasso to settings in which the points do not occur on a regular…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
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…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…
We consider tests of significance in the setting of the graphical lasso for inverse covariance matrix estimation. We propose a simple test statistic based on a subsequence of the knots in the graphical lasso path. We show that this…
In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…