ニューラルネットワークと線形回帰分析のハイブリッド解析法　　東京都２３区の給水量予測問題への適用

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  • A Hybrid Approach with Neural Networks and Linear Regression Analysis and Its Application to Predictions of the Volume of the Water Supply in District 23, Tokyo.
  • ニューラル ネットワーク ト センケイ カイキ ブンセキ ノ ハイブリッド カイセキホウ トウキョウト 23ク ノ キュウスイリョウ ヨソク モンダイ エ ノ テキヨウ
  • Its Application to Predictions of the Volume of the Water Supply in District 23, Tokyo
  • 東京都23区の給水量予測問題への適用

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The paper proposes a hybrid regression analysis with neural networks and the classical linear model which possesses both sufficient forecasting accuracy and interpretability. The proposed method utilizes outputs of hidden units in the initially fitted neural network model as additional explanatory variables of the consequent stepwise linear multiple regression, where sigmoid function is used for the output function of the hidden layer of the three layers feed-forward neural networks.<BR>We applied the proposed method to construction of a prediction model for the volume of the water supply in Districts 23, Tokyo to clarify our idea and the effectiveness of the method. Our approach automatically accounts unexpected structural changes in the output variable, i.e. the volume of the water supply, which seems to be related to the water leakage. The water leakage measurements were not observed before 1985 due to the inappropriate measurement method. When such bias from the measurement is adjusted by including the corresponding output from the neural networks, not only did the multiple correlation coefficient of the linear regression model increase drastically, but also the sign conditions of the regression coefficients became consistent. This means the proposed hybrid approach attains the interpretability of the data analysis.

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