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Generalized information potential criterion for adaptive system training.

D Erdogmus¹, J C Principe

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Summary

This summary is machine-generated.

This study generalizes Renyi

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Area of Science:

Adaptive Systems
Information Theory
Machine Learning

Background:

Supervised adaptive systems traditionally minimize error energy.
Renyi's error entropy offers an alternative cost function by minimizing information content.
Previous work introduced quadratic Renyi's error entropy.

Purpose of the Study:

To generalize the error entropy criterion using arbitrary order Renyi's entropy.
To incorporate flexible kernel functions for density estimation.
To validate the theoretical framework through simulations.

Main Methods:

Generalization of Renyi's error entropy for adaptive systems.
Kernel-based density estimation for error signal analysis.
Convolution smoothing and Parzen windowing for optimization.

Main Results:

The proposed entropy estimator preserves the global minimum of the actual entropy.
Demonstrated equivalence between convolution smoothing and kernel-based methods.
Successful application in time-series prediction and classification tasks.

Conclusions:

The generalized error entropy criterion provides a robust alternative cost function.
The method is effective for adaptive systems, enhancing prediction and classification.
This work expands the applicability of entropy-based learning methods.