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Using radial basis functions to approximate a function and its error bounds.

J A Leonard¹, M A Kramer, L H Ungar

¹Dept. of Chem. Eng., MIT, Cambridge, MA.

IEEE Transactions on Neural Networks

|January 1, 1992

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A new validity index network (VI net) was developed. This network improves function fitting and provides confidence intervals, highlighting areas where the model may not perform well.

Area of Science:

Machine Learning
Artificial Intelligence
Data Science

Background:

Radial basis function networks are widely used for function approximation.
Assessing the reliability of predictions, especially in regions of extrapolation, remains a challenge.

Purpose of the Study:

To introduce a novel network, the validity index network (VI net), for enhanced function fitting.
To develop a method for calculating confidence intervals that indicate prediction reliability.

Main Methods:

The VI net is derived from radial basis function networks.
The network is designed to fit complex functions.
It incorporates a mechanism to calculate confidence intervals for its outputs.

Main Results:

Related Experiment Videos

The VI net successfully fits functions across various datasets.
Confidence intervals generated by the VI net accurately identify regions of poor fit.
The network effectively flags areas of extrapolation where predictions are less reliable.

Conclusions:

The VI net offers a robust approach to function fitting with built-in reliability assessment.
It provides valuable insights into the local accuracy of predictions.
This network is a promising tool for applications requiring reliable function approximation and uncertainty quantification.