## 2 Methods
### Validation Procedures
#### 2.3.3 Assessing the Synthesized Data Accuracy  
We assessed the synthesized data accuracy by adopting the following three metrics: column shape, column pair trend, and overall quality score [27].  
Figure 2: Datasets used in this study. The original data are consumer survey data with a large sample size. The seed data are equivalent to the consumer survey data with a small sample size.  
each machine learning algorithm using each datum and its standard deviation. The average values of these evaluation metrics represent the predictive performance when using the data, while the standard deviation values depict the predictive performance stability. The useful data for the predictive analysis were easily assessed by organizing these values into a two-dimensional (2D) map and plotting each datum in it (Figure 4). The horizontal axis represents the predictive performance, which is the average value of the evaluation metrics, whereas the vertical axis denotes the stability concerning the evaluation metrics when conducting a predictive analysis, which comprises the standard deviation values for the evaluation metrics. These high average and low standard deviation values show the data qualities without depending on the abilities of machine learning algorithms under uniform conditions relative to the hyperparameters of the machine learning algorithms. This map shows that the data with the best predictive performance and the highest stability are the most useful data for prediction tasks in marketing analysis, regardless of the type of machine learning algorithm.  
In relation to the degree of concordance of the feature importance scores (Figure 5), the original data, which are the benchmark data, corresponded with Data A, while the other data, such as the seed and synthesized data, corresponded with Data B and C. We calculated the correlation coefficients (Pearson's r and Spearman's rho) between the original and other data based on the feature importance scores computed in each machine learning algorithm. These correlation coefficients imply the degree of concordance between the original and other data, validating whether or not the other data offer possibilities of alternatives to the original data when predicting outcomes and assessing the influential features for outcomes. While the data with higher correlation coefficient values might be a prospective alternative to the original data, those with low correlation coefficient values might be less desirable in terms of alternatives to the original data.  
To judge which dataset types and data are the most appropriate for marketing analysis, we propose 2D maps that organize the predictive performance results and the degree of concordance by the evaluation metrics (Figure 6). Similar to in Figure 4, the predictive performance was depicted on the horizontal axis. The degree of concordance, which can use the values of the averaged correlation coefficients based on Pearson r and Spearman rho, was set as the vertical axis. Thus, the higher the values on the horizontal axis, the better the results obtained using the concerned data in the machine learning algorithm calculation. The higher values on the vertical axis suggested a close pattern of the feature importance scores between the original and other data. In this map, the data with the best predictive performance and the closest feature importance scores between the original and other data were the most useful data for the marketing analysis.  
Figure 4: Conceptual predictive performance vs. stability map.