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Theoretical bounds of generalization error for generalized extreme learning machine and random vector functional link

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Summary

This study analyzes prediction errors in Generalized Extreme Learning Machines (GELM) and Random Vector Functional Networks (RVFL). It provides methods to calculate error bounds and tail probabilities for enhanced algorithm reliability.

Keywords:
Generalization errorGeneralized extreme learning machineMoore–Penrose generalized inverseRandom vector functional link networkTail probabilityTheoretical bound

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Area of Science:

  • Machine Learning
  • Computational Neuroscience

Background:

  • Theoretical analysis of learning algorithm prediction accuracy is essential for reliability.
  • Generalized Extreme Learning Machine (GELM) utilizes the Moore-Penrose generalized inverse (M-P GI) for output matrix enhancement.
  • Extreme Learning Machine (ELM) is a type of Random Vector Functional Link (RVFL) network lacking direct input-output links.

Purpose of the Study:

  • To analyze prediction errors in GELM using least square estimation.
  • To investigate tail probabilities for upper and lower error bounds.
  • To provide criteria for precise prediction error bounds and stochastically improved network environments.

Main Methods:

  • Analysis of tail probabilities for error bounds using L2 norm, Frobenius norm, stable rank, and M-P GI.
  • Extension of theoretical analysis to RVFL networks.
  • Application to simple examples and large-scale datasets for verification.

Main Results:

  • Formulas for immediately obtaining upper and lower bounds of prediction errors and their tail probabilities via matrix calculations in GELM and RVFL.
  • Demonstration of analysis and execution speed with big data.
  • Validation of theoretical analysis on diverse datasets.

Conclusions:

  • The study offers criteria for real-time assessment of network learning performance reliability.
  • It guides the selection of network structures for improved performance reliability.
  • The analytical method can inform error analysis in Deep Neural Networks (DNNs) using gradient descent.