Related papers: A convex pseudo-likelihood framework for high dime…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…
The curse of dimensionality is a recognized challenge in nonparametric estimation. This paper develops a new L0-norm regularization approach to the convex quantile and expectile regressions for subset variable selection. We show how to use…
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…
Growth in both size and complexity of modern data challenges the applicability of traditional likelihood-based inference. Composite likelihood (CL) methods address the difficulties related to model selection and computational intractability…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection,…
We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…
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…
Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
This article develops a framework for testing general hypothesis in high-dimensional models where the number of variables may far exceed the number of observations. Existing literature has considered less than a handful of hypotheses, such…
Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…
Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…