Related papers: Linear regression with partially mismatched data: …
Recently, there has been significant interest in linear regression in the situation where predictors and responses are not observed in matching pairs corresponding to the same statistical unit as a consequence of separate data collection…
A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units. A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled…
This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…
In regression analysis of multivariate data, it is tacitly assumed that response and predictor variables in each observed response-predictor pair correspond to the same entity or unit. In this paper, we consider the situation of "permuted…
We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar (1987). The idea is to generate a random finite subset of a parameter space which will…
We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…
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…
This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
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…
We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…
In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses…
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…
Deciding which predictors to use plays an integral role in deriving statistical models in a wide range of applications. Motivated by the challenges of predicting events across a telecommunications network, we propose a semi-automated, joint…