Related papers: Penalized Interaction Estimation for Ultrahigh Dim…
We consider the problem of learning a coefficient vector $x_{0}$ in $R^{N}$ from noisy linear observations $y=Fx_{0}+w$ in $R^{M}$ in the high dimensional limit $M,N$ to infinity with $\alpha=M/N$ fixed. We provide a rigorous derivation of…
Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an…
Adaptive nuclear-norm penalization is proposed for low-rank matrix approximation, by which we develop a new reduced-rank estimation method for the general high-dimensional multivariate regression problems. The adaptive nuclear norm of a…
Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…
We consider a class of distributed optimization problem where the objective function consists of a sum of strongly convex and smooth functions and a (possibly nonsmooth) convex regularizer. A multi-agent network is assumed, where each agent…
Stepped-wedge designs are increasingly used in randomized experiments to accommodate logistical and ethical constraints by staggering treatment roll-out over time. Despite their popularity, existing analytical methods largely rely on…
Heterogeneous panel data models that allow the coefficients to vary across individuals and/or change over time have received increasingly more attention in statistics and econometrics. This paper proposes a two-dimensional heterogeneous…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…
High-dimensional data can often display heterogeneity due to heteroscedastic variance or inhomogeneous covariate effects. Penalized quantile and expectile regression methods offer useful tools to detect heteroscedasticity in…
We propose a new weighted average estimator for the high dimensional parameters under the distributed learning system, in which the weight assigned to each coordinate is precisely proportional to the inverse of the variance of the local…
We propose some extensions to semi-parametric models based on Bayesian additive regression trees (BART). In the semi-parametric BART paradigm, the response variable is approximated by a linear predictor and a BART model, where the linear…
Dynamic treatment regimes (DTRs) consist of a sequence of decision rules, one per stage of intervention, that finds effective treatments for individual patients according to patient information history. DTRs can be estimated from models…
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…
Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…
Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high-dimensional covariates primarily…
We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one…
While including pairwise interactions in a regression model can better approximate response surface, fitting such an interaction model is a well-known difficult problem. In particular, analyzing contemporary high-dimensional datasets often…