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Related Concept Videos

Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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Classification of Signals

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Aggregates Classification

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Expected Frequencies in Goodness-of-Fit Tests01:19

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Quantifying and Rejecting Outliers: The Grubbs Test01:02

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Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is...

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Related Experiment Video

Updated: Jun 12, 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

On the complexity of discrete feature selection for optimal classification.

Jose M Peña1, Roland Nilsson

  • 1Department of Computer and Information Science, Linköping University, Linköping, Sweden. jospe@ida.liu.se

IEEE Transactions on Pattern Analysis and Machine Intelligence
|June 19, 2010
PubMed
Summary

This study analyzes feature selection complexity for discrete data. Finding a minimal Bayes risk subset of size k requires exhaustive search, but finding the absolute minimal subset is computationally feasible under certain conditions.

Related Experiment Videos

Last Updated: Jun 12, 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
  • Statistical Learning Theory
  • Computational Complexity

Background:

  • Classification problems with discrete features are common in machine learning.
  • Feature selection aims to identify the most informative features to improve model performance and reduce computational cost.
  • Assessing the complexity of feature selection is crucial for developing efficient algorithms.

Purpose of the Study:

  • To analyze the computational complexity of two distinct feature selection problems.
  • To determine the necessary search strategies for finding feature subsets with minimal Bayes risk.
  • To investigate the practical implications of these findings for discrete classification tasks.

Main Methods:

  • Theoretical analysis of feature selection problem complexity.
  • Demonstration of probability distributions to illustrate worst-case scenarios for subset risk ordering.
  • Development of insights into efficient search algorithms for minimal feature subsets.

Main Results:

  • Finding a feature subset of a specific size k with minimal Bayes risk necessitates an exhaustive search.
  • Finding the overall minimal feature subset with minimal Bayes risk is shown to be computationally tractable under mild assumptions.
  • The study provides a contrast in complexity between fixed-size and absolute minimal feature subset selection.

Conclusions:

  • The complexity of feature selection varies significantly depending on the specific objective (fixed size vs. absolute minimum).
  • Exhaustive search is unavoidable for fixed-size minimal Bayes risk feature subset selection.
  • Efficient algorithms can be developed for finding the absolute minimal feature subset, avoiding exhaustive search.