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Rate Distortion Theory for Descriptive Statistics.

ABSTRACT: Rate distortion theory was developed for optimizing lossy compression of data, but it also has applications in statistics. In this paper, we illustrate how rate distortion theory can be used to analyze various datasets. The analysis involves testing, identification of outliers, choice of compression rate, calculation of optimal reconstruction points, and assigning "descriptive confidence regions" to the reconstruction points. We study four models or datasets of increasing complexity: clustering, Gaussian models, linear regression, and a dataset describing orientations of early Islamic mosques. These examples illustrate how rate distortion analysis may serve as a common framework for handling different statistical problems.

SUBMITTER: Harremoes P

PROVIDER: S-EPMC10047654 | biostudies-literature | 2023 Mar

REPOSITORIES: biostudies-literature

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Rate Distortion Theory for Descriptive Statistics.

Harremoës Peter P

Entropy (Basel, Switzerland) 20230305 3

Rate distortion theory was developed for optimizing lossy compression of data, but it also has applications in statistics. In this paper, we illustrate how rate distortion theory can be used to analyze various datasets. The analysis involves testing, identification of outliers, choice of compression rate, calculation of optimal reconstruction points, and assigning "descriptive confidence regions" to the reconstruction points. We study four models or datasets of increasing complexity: clustering, ...[more]

PMID: 36981344

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Project description:BACKGROUND:The purpose of this study was to analyze the correlation between spatial resolution and ball distortion rate of panoramic radiography and to elucidate the minimum criterion for ball distortion rate, which is very relevant to clinical readability. METHODS:Horizontal and vertical spatial resolution and ball distortion rates were calculated in the same position, such as the incisor, premolar, molar, and temporomandibular joint area with various object depths corresponding to 48?mm. Three devices were evaluated. A region showing spatial resolution above the reference standard was selected, and the ball distortion rate corresponding to the same region was divided into horizontal and vertical phantom groups. The mean and standard deviation of the obtained ball distortion rates were calculated. Student's t-test was used to statistically analyze the mean difference in ball distortion rates between vertical and horizontal phantom groups. RESULTS:In all devices, the horizontal line pair phantom, but not the vertical line pair phantom, was readable in all areas measured at the line pair value of at least 1.88 lp/mm. The line pair value tended to be higher toward the center and lower toward the outside. The ball distortion rate tended to decrease closer to the center and increased further away. In addition, ball distortion rates could not be measured at some areas as they were not recognized as balls due to the high degree of distortion at the outermost and innermost sides. The number of balls satisfying the reference value using the horizontal line pair phantom was 102 (mean of ball distortion rates, 20.98; standard deviation, 15.25). The number of balls satisfying the reference value using the vertical line pair phantom was 49 (mean of ball distortion rates, 16.33; standard deviation, 14.25). However, mean ball distortion rate was not significantly different between the two groups. CONCLUSIONS:Image layer of panoramic radiography could be evaluated by the spatial resolution using horizontal and vertical line pair phantoms and by assessing ball distortion rates through a ball-type panorama phantom. A ball distortion rate of 20% could be used as a threshold to evaluate the image layer of panoramic radiography.

Dataset Information

Rate Distortion Theory for Descriptive Statistics.

Publications

Rate Distortion Theory for Descriptive Statistics.

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