Related papers: Honest confidence sets for high-dimensional regres…
Regression modeling is the workhorse of statistics and there is a vast literature on estimation of the regression function. It is realized in recent years that in regression analysis the ultimate aim may be the estimation of a level set of…
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
In this article the package High-dimensional Metrics (\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on…
Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…
Sparse training has emerged as a promising method for resource-efficient deep neural networks (DNNs) in real-world applications. However, the reliability of sparse models remains a crucial concern, particularly in detecting unknown…
Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…
Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix $X \in \mathbb{R}^{N \times d}$ and measurements or labels ${y} \in \mathbb{R}^N$ where ${y} = {X}…
In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…
In the present paper we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we…
Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of…
We develop a novel method to construct uniformly valid confidence bands for a nonparametric component $f_1$ in the sparse additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ in a high-dimensional setting. Our method integrates sieve…
In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold…
We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which…