Related papers: Linear Regression with Sparsely Permuted Data
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…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…
Among semiparametric regression models, partially linear additive models provide a useful tool to include additive nonparametric components as well as a parametric component, when explaining the relationship between the response and a set…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
This paper studies the problem of multivariate linear regression where a portion of the observations is grossly corrupted or is missing, and the magnitudes and locations of such occurrences are unknown in priori. To deal with this problem,…
We introduce a general framework for regression in the errors-in-variables regime, allowing for full flexibility about the dimensionality of the data, observational error probability density types, the (nonlinear) model type and the…
A common approach in forecasting problems is to estimate a least-squares regression (or other statistical learning models) from past data, which is then applied to predict future outcomes. An underlying assumption is that the same…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…
In many fields, and especially in the medical and social sciences and in recommender systems, data are gathered through clinical studies or targeted surveys. Participants are generally reluctant to respond to all questions in a survey or…
We study a regression problem where for some part of the data we observe both the label variable ($Y$) and the predictors (${\bf X}$), while for other part of the data only the predictors are given. Such a problem arises, for example, when…
Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…
We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…
We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according…