Related papers: Sparse Variable Selection on High Dimensional Hete…

This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…

We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on…

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…

Is it possible to find the sparsest vector (direction) in a generic subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S})= n < p$? This problem can be considered a homogeneous variant of the sparse recovery problem,…

We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is…

Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or…

High-dimensional data sets are often available in genome-enabled predictions. Such data sets include nonlinear relationships with complex dependence structures. For such situations, vine copula based (quantile) regression is an important…

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…

We develop a Bayesian tree ensemble model to estimate heterogeneous treatment effects in censored survival data with high-dimensional covariates. Instead of imposing sparsity through the tree structure, we place a horseshoe prior directly…

Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for…

Confounding matters in almost all observational studies that focus on causality. In order to eliminate bias caused by connfounders, oftentimes a substantial number of features need to be collected in the analysis. In this case, large p…

We propose an extensive simulation study to compare some variable selection procedures in a high-dimensional framework. Assuming that the relationship between the actives variables and the response variable is linear, the high-dimensional…

In this paper, we study transfer learning for high-dimensional factor-augmented sparse linear models, motivated by applications in economics and finance where strongly correlated predictors and latent factor structures pose major challenges…

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…

Tabular datasets with low-sample-size or many variables are prevalent in biomedicine. Practitioners in this domain prefer linear or tree-based models over neural networks since the latter are harder to interpret and tend to overfit when…

Model performance is frequently reported only for the overall population under consideration. However, due to heterogeneity, overall performance measures often do not accurately represent model performance within specific subgroups. We…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…

Panel data allows for the modeling of unobserved heterogeneity, significantly raising the number of nuisance parameters and making high dimensionality a practical issue. Meanwhile, temporal and cross-sectional dependence in panel data…