Linear regression with an unknown permutation: Statistical and computational limits

Pananjady, Ashwin; Wainwright, Martin J.; Courtade, Thomas A.

doi:10.1109/allerton.2016.7852261

Cited by 30 publications

(65 citation statements)

References 31 publications

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“…It can be shown that with σ 2 w being zero, equation (13) holds, which is consistent with the results obtained in [9].…”

Section: Holds Then the Summaries Of Sensor's Observationsỹ Are Sortsupporting

confidence: 90%

“…Remark 1 For the ML estimation problem (6) with σ 2 w = 0, a polynomial time algorithm is provided [9]. It can be shown that with σ 2 w being zero, equation (13) holds, which is consistent with the results obtained in [9].…”

Section: Holds Then the Summaries Of Sensor's Observationsỹ Are Sortsupporting

confidence: 78%

“…In the absence of noise, it is shown that as long as the number of measurements is twice as many as that of unknown parameters under random linear sensing strategy, exact recovery is possible [8]. While in [9], the observation noise is taken into account, and it is shown that recovery of permutation matrix depends sharply on the signal-to-noise ratio, the number of measurements and unknown parameters. In addition, It is shown that recovery of permutation matrix is NP-hard, while a polynomial time algorithm is provided for the scalar parameter estimation problem.…”

Section: Introductionmentioning

confidence: 98%

“…A variant, where the measurement matrix suffers from errors is also studied, and the corresponding maximum likelihood (ML) estimator can be found efficiently via numerical algorithms [3][4][5][6]. Recently, a parameter estimation problem where the observations are perturbed by an unknown permutation matrix has been studied extensively [7][8][9][10][11]. In [7], a branch and bound algorithm utilizing sparsity information is proposed and numerical results show that the unknown permutation can be correctly retrieved.…”

Section: Introductionmentioning

confidence: 98%

“…Zhu is studied. The main contribution is to propose an efficient iterative algorithm which works via sorting and is a variant of the one proposed for homoscedastic noise in [9]. Since the problem is strongly non-convex, our proposed algorithm usually converges to a local minima and the permutation matrix may not be exactly recovered.…”

Section: Introductionmentioning

confidence: 98%

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Parameter Estimation via Unlabeled Sensing Using Distributed Sensors

et al. 2017

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In this letter, the problem of estimating an unknown deterministic parameter is studied, where each sensor acquires a noisy version of the signal and the data at fusion center are unlabeled. Two scenarios are studied, one is that each sensor uses analog communication to transmit its observations with different channel coefficients. Another is that each sensor uses a different threshold to quantize the noisy signal with a transition matrix describing the channel. Sufficient conditions are provided under which maximum likelihood (ML) estimators can be found in polynomial time, and numerical simulations are conducted to evaluate performances of ML estimators.

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“…It can be shown that with σ 2 w being zero, equation (13) holds, which is consistent with the results obtained in [9].…”

Section: Holds Then the Summaries Of Sensor's Observationsỹ Are Sortsupporting

confidence: 90%

Section: Holds Then the Summaries Of Sensor's Observationsỹ Are Sortsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

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Parameter Estimation via Unlabeled Sensing Using Distributed Sensors

et al. 2017

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Robust regression using probabilistically linked data

Chambers

Fabrizi

Ranalli

et al. 2022

WIREs Computational Stats

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There is growing interest in a data integration approach to survey sampling, particularly where population registers are linked for sampling and subsequent analysis. The reason for doing this is simple: it is only by linking the same individuals in the different sources that it becomes possible to create a data set suitable for analysis. But data linkage is not error free. Many linkages are nondeterministic, based on how likely a linking decision corresponds to a correct match, that is, it brings together the same individual in all sources. High quality linking will ensure that the probability of this happening is high. Analysis of the linked data should take account of this additional source of error when this is not the case. This is especially true for secondary analysis carried out without access to the linking information, that is, the often confidential data that agencies use in their record matching. We describe an inferential framework that allows for linkage errors when sampling from linked registers. After first reviewing current research activity in this area, we focus on secondary analysis and linear regression modeling, including the important special case of estimation of subpopulation and small area means. In doing so we consider both robustness and efficiency of the resulting linked data inferences. This article is categorized under: Algorithms and Computational Methods > Maximum Likelihood Methods Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysisefficiency, exchangeable linkage error, finite population inference, linked data, regression, robust estimation | INTRODUCTIONData linkage is now an inextricable part of how data are obtained for analysis in modern science and public administration. The classical paradigm of first identifying a well-defined target population that can provide the data of interest and then measuring the values of the relevant variables for the individuals making up this population, or from a sample taken from it, is now often replaced by a data integration approach. This first links the records for the same individuals that are stored in the many population registers that are now available and then treats the resulting linked

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Spherical Regression Under Mismatch Corruption With Application to Automated Knowledge Translation

Shi

Cai

2020

Journal of the American Statistical Association

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Motivated by a series of applications in data integration, language translation, bioinformatics, and computer vision, we consider spherical regression with two sets of unit-length vectors when the data are corrupted by a small fraction of mismatch in the response-predictor pairs. We propose a three-step algorithm in which we initialize the parameters by solving an orthogonal Procrustes problem to estimate a translation matrix W ignoring the mismatch. We then estimate a mapping matrix aiming to correct the mismatch using hard-thresholding to induce sparsity, while incorporating potential group information. We eventually obtain a refined estimate for W by removing the estimated mismatched pairs. We derive the error bound for the initial estimate of W in both fixed and high-dimensional setting. We demonstrate that the refined estimate of W achieves an error rate that is as good as if no mismatch is present. We show that our mapping recovery method not only correctly distinguishes one-to-one and one-to-many correspondences, but also consistently identifies the matched pairs and estimates the weight vector for combined correspondence. We examine the finite sample performance of the proposed method via extensive simulation studies, and with application to the unsupervised translation of medical codes using electronic health records data.

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Linear regression with an unknown permutation: Statistical and computational limits

Cited by 30 publications

References 31 publications

Parameter Estimation via Unlabeled Sensing Using Distributed Sensors

Parameter Estimation via Unlabeled Sensing Using Distributed Sensors

Robust regression using probabilistically linked data

Spherical Regression Under Mismatch Corruption With Application to Automated Knowledge Translation

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