Related papers: Shuffled total least squares
Is it possible to perform linear regression on datasets whose labels are shuffled with respect to the inputs? We explore this question by proposing several estimators that recover the weights of a noisy linear model from labels that are…
This paper considers the sparse recovery with shuffled labels, i.e., $\by = \bPitrue \bX \bbetatrue + \bw$, where $\by \in \RR^n$, $\bPi\in \RR^{n\times n}$, $\bX\in \RR^{n\times p}$, $\bbetatrue\in \RR^p$, $\bw \in \RR^n$ denote the…
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…
The shuffled linear regression problem aims to recover linear relationships in datasets where the correspondence between input and output is unknown. This problem arises in a wide range of applications including survey data, in which one…
This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$,…
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…
This paper considers the task of linear regression with shuffled labels, i.e., $\mathbf Y = \mathbf \Pi \mathbf X \mathbf B + \mathbf W$, where $\mathbf Y \in \mathbb R^{n\times m}, \mathbf Pi \in \mathbb R^{n\times n}, \mathbf X\in \mathbb…
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
We propose to solve a label ranking problem as a structured output regression task. We adopt a least square surrogate loss approach that solves a supervised learning problem in two steps: the regression step in a well-chosen feature space…
In this paper, we study the problem of multivariate shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we investigate the model…
In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…
The assumption that response and predictor belong to the same statistical unit may be violated in practice. Unbiased estimation and recovery of true label ordering based on unlabeled data are challenging tasks and have attracted increasing…
Given a full rank matrix $X$ with more columns than rows, consider the task of estimating the pseudo inverse $X^+$ based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible…
In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…