Linear Regression without Correspondences via Concave Minimization

Peng, Liangzu; Tsakiris, Manolis C.

doi:10.48550/arxiv.2003.07706

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…Tsakiris and collaborators [20,21] have studied important theoretical aspects such as well-posedness from an algebraic perspective, and have also put forth practical computational schemes such as a branchand-bound algorithm (cf. also [30]) and concave maximization [31]. An approximate EM scheme with a Markov-Chain-Monte-Carlo (MCMC) approximation of the E-step is discussed in [17,32].…”

Section: Introductionmentioning

confidence: 99%

Estimation in exponential family Regression based on linked data contaminated by mismatch error

Wang¹,

Ben-David²,

Slawski³

2020

Preprint

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Identification of matching records in multiple files can be a challenging and error-prone task. Linkage error can considerably affect subsequent statistical analysis based on the resulting linked file. Several recent papers have studied post-linkage linear regression analysis with the response variable in one file and the covariates in a second file from the perspective of the "Broken Sample Problem" and "Permuted Data". In this paper, we present an extension of this line of research to exponential family response given the assumption of a small to moderate number of mismatches. A method based on observation-specific offsets to account for potential mismatches and 1 -penalization is proposed, and its statistical properties are discussed. We also present sufficient conditions for the recovery of the correct correspondence between covariates and responses if the regression parameter is known. The proposed approach is compared to established baselines, namely the methods by Lahiri-Larsen and Chambers, both theoretically and empirically based on synthetic and real data. The results indicate that substantial improvements over those methods can be achieved even if only limited information about the linkage process is available.

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Section: Introductionmentioning

confidence: 99%

Estimation in exponential family Regression based on linked data contaminated by mismatch error

Wang¹,

Ben-David²,

Slawski³

2020

Preprint

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“…• Some of the existing algorithms are of very high computational complexity, and can only handle small number of data points in low dimensions (Elhami et al, 2017;Pananjady et al, 2017a;Tsakiris et al, 2018;Peng and Tsakiris, 2020). Other algorithms choose to optimize with respect to w and π in an alteranting manner, e.g., alternating minimization in Abid et al (2017).…”

Section: Introductionmentioning

confidence: 99%

A Hypergradient Approach to Robust Regression without Correspondence

Xie,

Mao,

Zuo

et al. 2020

Preprint

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We consider a regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring instruments are unable to preserve the correspondence between the samples and the measurements. Due to the combinatorial nature, most of existing methods are only applicable when the sample size is small, and limited to linear regression models. To overcome such bottlenecks, we propose a new computational framework -ROBOT-for the shuffled regression problem, which is applicable to large data and complex models. Specifically, we propose to formulate the regression without correspondence as a continuous optimization problem. Then by exploiting the interaction between the regression model and the data correspondence, we propose to develop a hypergradient approach based on differentiable programming techniques. Such a hypergradient approach essentially views the data correspondence as an operator of the regression, and therefore allows us to find a better descent direction for the model parameter by differentiating through the data correspondence. ROBOT is quite general, and can be further extended to the inexact correspondence setting, where the input and output data are not necessarily exactly aligned. Thorough numerical experiments show that ROBOT achieves better performance than existing methods in both linear and nonlinear regression tasks, including real-world applications such as flow cytometry and multi-object tracking.

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Linear Regression without Correspondences via Concave Minimization

Cited by 2 publications

References 26 publications

Estimation in exponential family Regression based on linked data contaminated by mismatch error

Estimation in exponential family Regression based on linked data contaminated by mismatch error

A Hypergradient Approach to Robust Regression without Correspondence

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