Correlation coefficient

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement. As tools of analysis, correlation coefficients present certain problems, including the propensity of some types to be distorted by outliers and the possibility of incorrectly being used to infer a causal relationship between the variables (for more, see Correlation does not imply causation). Types There are several different measures for the degree of correlation in data, depending on the kind of data: p

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MATH-234(a): Probability and statistics

Ce cours est une introduction à la théorie des probabilités et aux méthodes statistique.

DH-406: Machine learning for DH

This course aims to introduce the basic principles of machine learning in the context of the digital humanities. We will cover both supervised and unsupervised learning techniques, and study and implement methods to analyze diverse data types, such as images, music and social network data.

MATH-234(b): Probability and statistics

Le cours présente les notions de base de la théorie des probabilités et de l'inférence statistique. L'accent est mis sur les concepts principaux ainsi que les méthodes les plus utilisées.

Efficiently Maintaining Distributed Model-Based Views on Real-Time Data Streams

Karl Aberer, Petre Alexandru Arion, Ho Young Jeung, Sebastian Michel

Minimizing communication cost is a fundamental problem in large-scale federated sensor networks. Existing solutions applicable for the problem are often ad-hoc for specific query types, or they are inefficient when query results contain large volumes of data to be transferred over the networks. Maintaining model-based views of data streams has been recently highlighted because it permits the data communication over networks to be efficient by transmitting parameter values for the models, instead of sending original data streams. This paper proposes a novel framework that employs the advantages of using model-based views for communication-efficient stream data processing over federated sensor networks, yet it significantly improves state-of-the-art approaches. The framework is generic and any time-parameterized models can be plugged, as well as accuracy guarantees for query results are ensured throughout the large-scale networks. In addition, we boost the performance of the framework by the coded model update that enables efficient model update from one node to another. It predetermines parameter values for the model, updates only identifiers of the parameter values, and compresses the identifiers by utilizing bitmaps. Moreover, we propose a novel correlation model, named coded inter-variable model, that integrates the efficiency of the coded model update into more precise predictions of correlated models. Empirical studies with real data demonstrate that our proposal achieves substantial amounts of communication reduction, outperforming a state-of-the art method.

2011

Efficiently Maintaining Distributed Model-Based Views on Real-Time Data Streams

Karl Aberer, Petre Alexandru Arion, Ho Young Jeung

Minimizing communication cost is a fundamental problem in large-scale federated sensor networks. Maintaining model-based views of data streams has been highlighted because it permits efficient data communication by transmitting parameter values of models, instead of original data streams. We propose a framework that employs the advantages of using model-based views for communication-efficient stream data processing over federated sensor networks, yet it significantly improves state-of-the-art approaches. The framework is generic and any time-parameterized models can be plugged, while accuracy guarantees for query results are ensured throughout the large-scale networks. In addition, we boost the performance of the framework by the coded model update that enables efficient model update from one node to another. It predetermines parameter values for the model, updates only identifiers of the parameter values, and compresses the identifiers by utilizing bitmaps. Moreover, we propose a correlation model, named coded inter-variable model, that merges the efficiency of the coded model update with that of correlation models. Empirical studies with real data demonstrate that our proposal achieves substantial amounts of communication reduction, outperforming state-of-the art methods.

IEEE2011

Age- and sex-specific normative values of bone mineral density in the adult glenoid

Philippe Büchler, Alain Farron, Dominique Pioletti, Alexandre Terrier, Frédéric Vauclair

The objective of this study was to determine the normative bone mineral density (BMD) of cortical and trabecular bone regions in the adult glenoid and its dependence on the subject's age and sex. We analyzed computed tomography (CT) scans of 441 shoulders (310 males, 18-69 years) without any signs of glenohumeral joint pathology. Glenoid BMD was automatically quantified in six volumes of interest (VOIs): cortical bone (CO), subchondral cortical plate (SC), subchondral trabecular bone (ST), and three adjacent layers of trabecular bone (T1, T2, and T3). BMD was measured in Hounsfield unit (HU). We evaluated the association between glenoid BMD and sex and age with the Student's t test and Pearson's correlation coefficient (r), respectively. The lambda-mu-sigma method was used to determine age- and sex-specific normative values of glenoid BMD in cortical (CO and SC) and trabecular (ST, T1, T2, and T3) bone. Glenoid BMD was higher in males than females, in most age groups and most VOIs. Before 40 years old, the effect of age on BMD was very weak in both males and females. After 40 years old, BMD declined over time in all VOIs. This BMD decline with age was greater in females (cortical: r = -0.45, trabecular: r = -0.41) than in males (cortical: r = -0.30; trabecular: r = -0.32). These normative glenoid BMD values could prove clinically relevant in the diagnosis and management of patients with various shoulder disorders, in particular glenohumeral osteoarthritis and shoulder arthroplasty or shoulder instability, as well as in related research.

WILEY2022

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may i

Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variab