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Related Concept Videos

Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Regression Analysis01:11

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
Correlation and Regression00:53

Correlation and Regression

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 negative...
Regression Toward the Mean01:52

Regression Toward the Mean

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 researchers try to extrapolate results...
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).

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Related Experiment Video

Updated: May 9, 2026

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
07:35

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

Is mutual information adequate for feature selection in regression?

Benoît Frénay1, Gauthier Doquire, Michel Verleysen

  • 1Machine Learning Group - ICTEAM, Université catholique de Louvain, Place du Levant 3, 1348 Louvain-la-Neuve, Belgium.

Neural Networks : the Official Journal of the International Neural Network Society
|July 30, 2013
PubMed
Summary
This summary is machine-generated.

Mutual information feature selection is linked to minimizing regression errors like mean squared error. However, this method can fail in specific scenarios, necessitating careful application for optimal results.

Keywords:
Feature selectionMAEMSEMutual informationRegression

Related Experiment Videos

Last Updated: May 9, 2026

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
07:35

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

Area of Science:

  • Machine Learning
  • Data Science
  • Statistics

Background:

  • Feature selection is crucial for high-dimensional regression.
  • Mutual information is a common criterion for feature selection.
  • A link between mutual information and regression error criteria is missing.

Purpose of the Study:

  • Establish a theoretical connection between mutual information and regression error criteria.
  • Investigate the conditions under which mutual information optimally selects features for regression.
  • Provide guidance for the practical application of mutual information in feature selection.

Main Methods:

  • Theoretical analysis of feature selection criteria.
  • Mathematical derivations linking mutual information to mean squared error and mean absolute error.
  • Characterization of scenarios where mutual information may not yield optimal feature subsets.

Main Results:

  • Demonstrated that mutual information selection minimizes mean squared error and mean absolute error under certain assumptions.
  • Identified specific situations where the mutual information criterion can fail to select optimal features.
  • Provided theoretical groundwork for understanding the efficacy of mutual information in regression.

Conclusions:

  • Mutual information is a theoretically sound criterion for feature selection in regression, aligning with error minimization goals.
  • Awareness of potential failure cases is essential for effective practical implementation.
  • This work facilitates a more critical and efficient use of mutual information for feature selection in machine learning.