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Frequency-dependent Selection

Frequency-dependent Selection

When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to as frequency-dependent selection. Frequency-dependent selection may occur between species or within a single species. This type of selection can either be positive—with more common phenotypes having higher fitness—or negative, with rarer phenotypes conferring increased fitness.

Expected Frequencies in Goodness-of-Fit Tests

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).

Multiple Comparison Tests

Multiple Comparison Tests

Multiple comparison test, abbreviated as MCT, is a post hoc analysis generally performed after comparing multiple samples with one or more tests. An MCT will help identify a significantly different sample among multiple samples or a factor among multiple factors.
It would be easy to compare two samples using a significance alpha level of 0.05. In other words, there is only one sample pair to be compared. However, it would be difficult to identify a significantly different sample if the number...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

Routh-Hurwitz Criterion I

Routh-Hurwitz Criterion I

Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...

Routh-Hurwitz Criterion II

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...

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Related Experiment Video

Updated: Apr 12, 2026

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

On the feature selection criterion based on an approximation of multidimensional mutual information.

Kiran S Balagani¹, Vir V Phoha

¹Center for Secure Cyberspace, Computer Science,Louisiana Tech University, Nethken Hall, 600 W. Arizona Ave., Ruston,LA 71272, USA. ksb011@latech.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence

|May 22, 2010

Summary

This study derives a feature selection criterion using multidimensional mutual information. The criterion

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Area of Science:

Machine Learning
Statistical Modeling

Background:

Feature selection is crucial for building efficient and accurate predictive models.
Existing criteria often lack rigorous validation of underlying assumptions.

Purpose of the Study:

To derive and validate a feature selection criterion from multidimensional mutual information.
To provide a mathematical justification for the criterion's utility in classification tasks.

Main Methods:

Derivation of the feature selection criterion from multidimensional mutual information between features and class labels.
Specification and validation of lower-order dependency assumptions inherent in the criterion.
Mathematical analysis relating the criterion to Bayes classification error.

Main Results:

A novel feature selection criterion is derived.
The criterion's lower-order dependency assumptions are rigorously specified and validated.
The criterion's utility is mathematically linked to minimizing Bayes classification error.

Conclusions:

The derived feature selection criterion offers a theoretically sound approach.
Validation of assumptions and mathematical justification enhance its applicability in machine learning.