Related papers: Implementable confidence sets in high dimensional …

For regression model selection via maximum likelihood estimation, we adopt a vector representation of candidate models and study the likelihood ratio confidence region for the regression parameter vector of a full model. We show that when…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…

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…

We consider a linear regression model with regression parameter beta =(beta_1, ..., beta_p) and independent and identically N(0, sigma^2)distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…

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…

The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…

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…

We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…

We study asymptotically normal estimation and confidence regions for low-dimensional parameters in high-dimensional sparse models. Our approach is based on the $\ell_1$-penalized M-estimator which is used for construction of a bias…

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…

In recent years the ultrahigh dimensional linear regression problem has attracted enormous attentions from the research community. Under the sparsity assumption most of the published work is devoted to the selection and estimation of the…

Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for…

Performing statistical inference in high-dimension is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional estimators. Here, we consider linear regression in…

We study the problem of learning a high-density region of an arbitrary distribution over $\mathbb{R}^d$. Given a target coverage parameter $\delta$, and sample access to an arbitrary distribution $D$, we want to output a confidence set $S…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

Interpretability is often pointed out as a key requirement for trustworthy machine learning. However, learning and releasing models that are inherently interpretable leaks information regarding the underlying training data. As such…

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 the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…