An article in Scientia Iranica [Tuning the Parameters of an Artificial Neural Network (ANN) Using Central Composite

An article in Scientia Iranica [€œTuning the Parameters of an Artificial Neural Network (ANN) Using Central Composite Design and Genetic Algorithm€ (2011, Vol. 18(6), pp. 1600€“608)], described a series of experiments to tune parameters in artificial neural networks. One experiment considered the relationship between model fitness [measured by the square root of mean square error (RMSE) on a separate test set of data] and model complexity that were controlled by the number of nodes in the two hidden layers. The following data table (extracted from a much larger data set) contains three different ANNs: ANN1 has 33 nodes in layer 1 and 30 nodes in layer 2, ANN2 has 49 nodes in layer 1 and 45 nodes in layer 2, and ANN3 has 17 nodes in layer 1 and 15 nodes in layer 2.

(a) Construct a box plot to compare the different ANNs.

(b) Perform the analysis of variance with α = 0.05. What is the P-value?

(c) Analyze the residuals from the experiment.

(d) Calculate a 95% confi dence interval on RMSE for ANN2.

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ANN type ANNI RMSE 0.0391 0.0121 0.0132 0.0003 0.0023 0.0011 0.0054 0.0014 0.0006 0.022 0.0031 0.0019 ANN2 0.0007 ANN3 0.2227 0.0953 1.3892 1.7916 0.1992 0.1562 0.8911 0.0154