On Estimation under Noisy Order Statistics

Dytso, Alex; Cardone, Martina; Veedu, Mishfad Shaikh; Poor, H. Vincent

doi:10.1109/isit.2019.8849813

Cited by 14 publications

(5 citation statements)

References 21 publications

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“…Permutation associated estimation problems have recently gained significant importance and are studied in various fields [4]- [18]. The ranking (e.g., data permutation) estimation problem under a joint Gaussian distribution was investigated in [4]- [7].…”

Section: A Related Workmentioning

confidence: 99%

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Recovering Data Permutations From Noisy Observations: The Linear Regime

Jeong

Dytso

Cardone

et al. 2020

IEEE J. Sel. Areas Inf. Theory

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This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator followed by a sorting operation) is used. The derived expression holds with minimal assumptions on the distribution of X and when the noise has memory. Second, for the case of isotropic noise (i.e., noise with a diagonal scalar covariance matrix), the rates of convergence of the probability of error are characterized in the high and low noise regimes. In the low noise regime, for every dimension n, the probability of error is shown to behave proportionally to σ, where σ is the noise standard deviation. Moreover, the slope is computed exactly for several distributions and it is shown to behave quadratically in n. In the high noise regime, for every dimension n, the probability of correctness is shown to behave as 1/σ, and the exact expression for the rate of convergence is also provided.

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Section: A Related Workmentioning

confidence: 99%

“…A generalized framework of unlabeled sensing was presented in [15]- [17]. The estimation of a sorted vector based on noisy observations was proposed in [18], where the MMSE estimator on sorted data was characterized as a linear combination of estimators on the unsorted data.…”

Section: A Related Workmentioning

confidence: 99%

Recovering Data Permutations From Noisy Observations: The Linear Regime

Jeong

Dytso

Cardone

et al. 2020

IEEE J. Sel. Areas Inf. Theory

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“…In particular, the goal of [2] is to estimate the permutation that matches two sets of features given noisy observations. As another example, in [3] the authors propose a framework to estimate the values of an original sorted vector, given a noisy sorted observation of it. They show that, under certain symmetry conditions, the minimum mean square error estimator can be characterized by a linear combination of estimators on the unsorted data.…”

Section: A Related Workmentioning

confidence: 99%

Recovering Data Permutations from Noisy Observations: The Linear Regime

Jeong¹,

Dytso²,

Cardone³

et al. 2020

Preprint

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This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy data observation, according to which permutation was the original data sorted?The focus is on scenarios where data is generated according to an isotropic Gaussian distribution, and the perturbation consists of adding Gaussian noise with an arbitrary covariance matrix. This problem is posed within a hypothesis testing framework. The objective is to study the linear regime in which the optimal decoder has a polynomial complexity in the data size, and it declares the permutation by simply computing a linear function of the noisy observation.The main result of the paper is a complete characterization of the linear regime in terms of the noise covariance matrix. Specifically, it is shown that this matrix must have a very flat spectrum with at most three distinct eigenvalues to induce the linear regime. Several practically relevant implications of this result are discussed, and the error probability incurred by the decision criterion in the linear regime is also characterized. A core technical component consists of using linear algebraic and geometric tools, such as Steiner symmetrization.

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“…коло проблем, пов'язаних з вивченням їхніх фундаментальних властивостей і різноманіттям застосувань в обробці інформації [5,6,7]. Помітне місце в цих роботах займають перетворення абсолютно неперервних випадкових величин [8], які, крім практичної спрямованості, надають можливість вивчення та формалізації властивостей цього нелінійного методу обробки даних.…”

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Multichannel Convertion of Random Data With the Pair-Elements of Ordered Samples

Mazmanian¹

2021

Teh. elektrodin.

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The concept of multichannel parallel converting of probability density function (pdf) of random data was previously used for single-element pdf-converters. In development of this concept, here we investigate converting properties of spdf-converters channels formed by the sum of the pairs of ordered sample elements (order statistics). The characteristics of the conversion results as dependencies on the size of the samples and the displacement of the channels relative to the median of the samples were obtained for data with a uniform distribution density. Also where excluded the areas of mutual dependence of the density functions of the summed elements, which further where normalized together with approximating them functions. Despite the apparent structural differences, the goal of this study still was to determine the closeness of the converted data with some standard functions of the probability distribution density, in particular, with the normal distribution law. As before, the estimates of the closeness of the spdf-converter channels were obtained using the chi-square criteria. The results of the research were used to determine the size and location of the statistical closeness windows, and to construct spdf-converters statistical model. References 20, figures 14.

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On Estimation under Noisy Order Statistics

Cited by 14 publications

References 21 publications

Recovering Data Permutations From Noisy Observations: The Linear Regime

Recovering Data Permutations From Noisy Observations: The Linear Regime

Recovering Data Permutations from Noisy Observations: The Linear Regime

Multichannel Convertion of Random Data With the Pair-Elements of Ordered Samples

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