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Empirical strategy for stretching probability distribution in neural-network-based regression.

Eunho Koo1, Hyungjun Kim2

  • 1Center for Mathematical Analysis and Computation, Yonsei University, Seoul, South Korea; LTS, Inc., Tokyo, Japan.

Neural Networks : the Official Journal of the International Neural Network Society
|March 23, 2021
PubMed
Summary

We introduce weighted empirical stretching (WES), a novel loss function for artificial neural networks that improves prediction accuracy by increasing distribution overlap. WES enhances performance across various data distributions and noise levels.

Keywords:
DistributionLoss functionMultilayer perceptronNoisy input signalPrediction error

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Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Statistical Modeling

Background:

  • Prediction performance in artificial neural networks (ANNs) relies heavily on optimal weight determination between layers.
  • The choice of loss function significantly impacts ANN performance during back-propagation and gradient descent optimization.
  • Existing loss functions may not adequately address distribution inconsistencies between predicted values and true labels.

Purpose of the Study:

  • To propose a novel loss function, weighted empirical stretching (WES), designed to enhance prediction accuracy in ANNs.
  • To address distribution error by increasing the overlap between predicted and label distributions.
  • To develop a loss function applicable to diverse label distribution shapes and robust to noise.

Main Methods:

  • Introduced weighted empirical stretching (WES), a loss function measuring distribution error as the inconsistency between predicted and label distributions.
  • WES aims to maximize the overlap area of these distributions, incorporating a scaling hyperparameter (β).
  • Tested WES using feedforward neural networks with Fourier-extracted data from various ideal label distributions (unimodal, skewed unimodal, bimodal, skewed bimodal) under different noise levels.

Main Results:

  • Weighted empirical stretching (WES) generally outperformed commonly used loss functions in regression tasks.
  • The proposed WES loss function demonstrated robustness across various noise levels.
  • Significant improvements in Root Mean Square Error (RMSE) were observed in the extreme domains (tail regions) of the distribution.

Conclusions:

  • WES offers a superior approach to loss function design in ANNs by focusing on distribution overlap.
  • The method's effectiveness across diverse distributions and noise levels highlights its versatility.
  • The enhanced performance in predicting extreme values suggests potential applications in forecasting abnormal events in complex systems like natural disasters and financial markets.