## 4 Experimental Results
### Experimental Results  
The main objective of the following experiments was to show whether generated essays were useful as training data for AES systems. Since building an AES system was not the main concern of this study, we employed a simple deep learning architecture for AES systems. The BERT model with an additional layer for producing essay scores was the AES system used in these experiments. Since EssayGAN can automatically generate essays, our AES system was fine-tuned using both real and generated essays.  
In the experiments, we adopted the quadratic weighted kappa (QWK) value [20], which is widely used as a de facto standard metric. It measures the agreement of scoring between human raters and AES systems and varies from 0 (random agreement) to 1 (compete agreement). It is defined in Equation (8).  
\[k=1-\frac{\sum_{i,j}W_{i,j}O_{i,j}}{\sum_{i,j}W_{i,j}E_{i,j}}, \tag{8}\]  
where \(O_{i,j}\) of matrix \(O\) is the number of essays that receive a rating \(i\) from a human rater and a rating \(j\) from an AES system. The matrix \(E\) is the outer product of the vectors of human ratings and system ratings. The weight entries of matrix \(W\) are the differences between rater scores, calculated by \(W_{i,j}=\frac{(i-j)^{2}}{(N-1)^{2}}\), where \(N\) is the number of possible ratings and \(i\) and \(j\) are the human rating and the system rating, respectively.  
To evaluate our approach, we carried out a fivefold cross validation of the ASAP dataset in the same way as in [21; 22].  
Table 6 summarizes the comparison of QWK correlation according to the data augmentation techniques. The baseline is the QWK correlation of the model trained exclusively on the training data. The simple data-augmentation methods, Random and RandomOrder, were not useful for the AES system. The performances of those methods were lower than that of the baseline.  
From the perspective of data augmentation, EssayGAN performed better than Random and RandomOrder. In addition, EssayGAN outperformed EssayGAN without the \(t\)-step. This indicates that EssayGAN can mitigate the catastrophic forgetting problem that is pervasive during the fine-tuning process when adopting \(t\)-step of Algorithm 1.  
CS-GAN [5] is designed to generate new sentences tagged with category information. It has three sub-networks: a generator, a discriminator, and a classifier. To compare EssayGAN with other GAN models, we exploited CS-GAN, in which the classifier is replaced by a scorer to generate new essays rated with score information. The performance of the AES system trained on data augmented by CS-GAN was worse than that of the baseline model. Data augmentation by CS-GAN applied to only source-dependent prompts 3-6, with a small scale of scores in this work. (The data augmentation by CS-GAN for prompts 1, 2, 7, and 8 did not work properly, so we did not include the results for these processes. These prompts required CS-GAN to generate argumentative or narrative essays of 250-650 words. This task seemed to be too difficult for CS-GAN with only one generator).  
Table 7 shows a performance comparison with the state-of-the-art AES systems. Our AES system has the same architecture as 'BERT-CLS' from [8]; however, it can be trained with more training data thanks to EssayGAN. The R\({}^{2}\)BERT model achieved the best performance among the comparative models by adopting a multi-loss learning strategy. Our AES system achieved the second best performance on average. Based on the experimental results shown in Table 7, we found that the more training data were augmented elaborately by EssayGAN, the better the performance of the AES system, and this performance could be improved up to the level of the state-of-the-art AES models.  
In Table 1 of Appendix B, we present examples of the automatically generated essays for prompt 3.