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Correlation and Regression00:53

Correlation and Regression

1.2K
In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
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Correlations02:20

Correlations

32.8K
Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Coefficient of Correlation01:12

Coefficient of Correlation

6.1K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
6.1K
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
1.6K
Correlation01:09

Correlation

11.7K
In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
11.7K
Regression Toward the Mean01:52

Regression Toward the Mean

6.3K
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Related Experiment Video

Updated: Jun 23, 2025

Machine Learning Algorithms for Early Detection of Bone Metastases in an Experimental Rat Model
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Machine Learning Algorithms for Early Detection of Bone Metastases in an Experimental Rat Model

Published on: August 16, 2020

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Correlations of Cross-Entropy Loss in Machine Learning.

Richard Connor1, Alan Dearle1, Ben Claydon1

  • 1School of Computer Science, University of St Andrews, St Andrews KY16 9SS, UK.

Entropy (Basel, Switzerland)
|June 26, 2024
PubMed
Summary
This summary is machine-generated.

Cross-entropy loss in deep learning correlates strongly with triangular divergence and Euclidean distance over logits. This suggests triangular divergence as a cost-effective alternative and validates using Euclidean distance for logit similarity in classification.

Keywords:
Jensen–Shannon divergenceKullback–Leibler divergencecross-entropyf-divergencesoftmaxtriangular divergence

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Area of Science:

  • Machine Learning
  • Deep Neural Networks
  • Information Theory

Background:

  • Cross-entropy loss is fundamental for training deep neural networks.
  • Understanding relationships between loss functions can optimize training and feature extraction.

Purpose of the Study:

  • To investigate novel correlations between cross-entropy and other divergence functions.
  • To explore the relationship between cross-entropy and Euclidean distance over logits.
  • To identify potential computational efficiencies and new feature representations.

Main Methods:

  • Empirical observation of correlations between divergence functions.
  • Mathematical analysis of related divergence functions and softmax outputs.
  • Analysis of cross-entropy, triangular divergence, and Euclidean distance over logits.

Main Results:

  • Demonstrated near-perfect correlation between cross-entropy and triangular divergence in certain scenarios.
  • Showcased strong correlation between cross-entropy and Euclidean distance on softmax-derived logits.
  • Established that logits can be effectively treated as features in a Euclidean space.

Conclusions:

  • Triangular divergence presents a computationally cheaper alternative to cross-entropy loss.
  • Euclidean distance over logits is a valid and synergistic measure of similarity for networks trained with softmax and cross-entropy.
  • These findings offer practical implications for optimizing deep learning model training and analysis.