Related papers: High-dimensional estimation with geometric constra…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…
Suppose that we wish to estimate a vector $\mathbf{x} \in \mathbb{C}^n$ from a small number of noisy linear measurements of the form $\mathbf{y} = \mathbf{A x} + \mathbf{z}$, where $\mathbf{z}$ represents measurement noise. When the vector…
We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension…
We consider hypotheses testing problems for three parameters in high-dimensional linear models with minimal sparsity assumptions of their type but without any compatibility conditions. Under this framework, we construct the first…
We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
Let $(Y,(X_i)_{i\in\mathcal{I}})$ be a zero mean Gaussian vector and $V$ be a subset of $\mathcal{I}$. Suppose we are given $n$ i.i.d. replications of the vector $(Y,X)$. We propose a new test for testing that $Y$ is independent of…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
This paper studies nonparametric series estimation and inference for the effect of a single variable of interest x on an outcome y in the presence of potentially high-dimensional conditioning variables z. The context is an additively…
Completely randomized experiment is the gold standard for causal inference. When the covariate information for each experimental candidate is available, one typical way is to include them in covariate adjustments for more accurate treatment…
We consider the problem of estimating the conditional mean of a real Gaussian variable $\nolinebreak Y=\sum_{i=1}^p\nolinebreak\theta_iX_i+\nolinebreak \epsilon$ where the vector of the covariates $(X_i)_{1\leq i\leq p}$ follows a joint…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the…
This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…
Estimating signals underlying noisy data is a significant problem in statistics and engineering. Numerous estimators are available in the literature, depending on the observation model and estimation criterion. This paper introduces a…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive…
In this article, we propose a penalized high dimensional semiparametric model average quantile prediction approach that is robust for forecasting the conditional quantile of the response. We consider a two-step estimation procedure. In the…