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H. Wilson . F. Recknagel
The effect of moving from the same day structure to the time delay structure
varied according to the ca se study. In the case of the Myponga and Burrinjuck
reservoir models, the time delay structure brought about a considerable
improvement in prediction quality. These models achieved the correct forecasting
of the onset of bloom events (e.g., in 1993 for the Myponga model in Figure
14.4d, and in 1983 for the Burrinjuck model in Figure 14.6b). There was also
some improvement in the Darling River model, although there was generally some
delay in the forecasting of bloom on set (e.g. blooms in 1980/81 and 1985). The
other 3 case studies (Lake Biwa, Lake Kasumigaura, and Lake Soyang) fared
worse as a result of the time delay structure, with an increasing number of false
positive predictions, and a failure to predict the magnitude of events as effectively.
Figures 14.7 and 14.8 show the effects of the number of hidden nodes and the
stopping error of training on the RMS error of test set predictions for all models.
The box and whisker plots illustrate the distribution of RMS error for each
treatment, with the centre line of the box representing the median error, the top
and bottom lines representing interquartile ranges, and the whiskers extending to
the full ranges of the distributions. Outliers are represented by circles. The dotted
lines of these plots show the RMS error for the bootstrap aggregate model. The
boxplots indicate a rising error at low stopping errors and 5 hidden nodes for all
models except Lake Burrinjuck (Figures 14.7c and 14.7d). This is indicative of
the onset of overfitting in each of these cases. The Lake Soyang models also
displays overfitting at 2 hidden nodes (Figures 14.8e and 14.8f). The bootstrap
aggregate model is in general not prone to overfitting as indicated by a resistance
to the rising trend of the boxplots in most cases (although there is a rising trend for
the Lake Soyang bootstrap aggregate model).
Figures 14.9 and 14.10 illustrate the time series of the distributions of model
predictions for the Myponga 0 hidden node and 5 hidden node models respectively
(each trained with 0 error tolerance). With 0 hidden nodes, the very small
boxplots and the lack of outliers are indicative of low model variance. The 5
hidden node structure on the other hand is prone to very high model variance as
indicated by the much larger boxplots and wide spread outliers. However, the
aggregate model of the 5 hidden node structure, as illustrated by the centre lines of
the boxplots, remains close to the observed algal abundance values (Figure
14.10a).
H. Wilson . F. Recknagel
The effect of moving from the same day structure to the time delay structure
varied according to the ca se study. In the case of the Myponga and Burrinjuck
reservoir models, the time delay structure brought about a considerable
improvement in prediction quality. These models achieved the correct forecasting
of the onset of bloom events (e.g., in 1993 for the Myponga model in Figure
14.4d, and in 1983 for the Burrinjuck model in Figure 14.6b). There was also
some improvement in the Darling River model, although there was generally some
delay in the forecasting of bloom on set (e.g. blooms in 1980/81 and 1985). The
other 3 case studies (Lake Biwa, Lake Kasumigaura, and Lake Soyang) fared
worse as a result of the time delay structure, with an increasing number of false
positive predictions, and a failure to predict the magnitude of events as effectively.
Figures 14.7 and 14.8 show the effects of the number of hidden nodes and the
stopping error of training on the RMS error of test set predictions for all models.
The box and whisker plots illustrate the distribution of RMS error for each
treatment, with the centre line of the box representing the median error, the top
and bottom lines representing interquartile ranges, and the whiskers extending to
the full ranges of the distributions. Outliers are represented by circles. The dotted
lines of these plots show the RMS error for the bootstrap aggregate model. The
boxplots indicate a rising error at low stopping errors and 5 hidden nodes for all
models except Lake Burrinjuck (Figures 14.7c and 14.7d). This is indicative of
the onset of overfitting in each of these cases. The Lake Soyang models also
displays overfitting at 2 hidden nodes (Figures 14.8e and 14.8f). The bootstrap
aggregate model is in general not prone to overfitting as indicated by a resistance
to the rising trend of the boxplots in most cases (although there is a rising trend for
the Lake Soyang bootstrap aggregate model).
Figures 14.9 and 14.10 illustrate the time series of the distributions of model
predictions for the Myponga 0 hidden node and 5 hidden node models respectively
(each trained with 0 error tolerance). With 0 hidden nodes, the very small
boxplots and the lack of outliers are indicative of low model variance. The 5
hidden node structure on the other hand is prone to very high model variance as
indicated by the much larger boxplots and wide spread outliers. However, the
aggregate model of the 5 hidden node structure, as illustrated by the centre lines of
the boxplots, remains close to the observed algal abundance values (Figure
14.10a).