## 2 Materials and Methods
### Predict Age Information of the Unlabeled Dataset
#### 2.3.3 Train the Age Predictor  
In this step, the best prediction technique, identified in the previous subsection, was used to train a prediction model from the labeled dataset (i.e., the age predictor). Then, the multi-label target of each news article, \(\textit{agescore}_{\textit{news}}(n)\), in the labeled dataset was predicted using the learned age predictor. The predicted \(\textit{agescore}_{\textit{news}}(n,g)\) values of the estimated multi-label target were transformed into the \(\textit{agerate}_{\textit{news}}(n,g)\) values of the labeled news article through two substeps. First, going through the inverse way of Equation (4), and second, normalizing into unity (i.e., the sum across all age groups of a news article \(n\) becomes 1). Lastly, the obtained \(\textit{agerate}_{\textit{news}}(n,g)\) values were compared with the corresponding true values of the labeled dataset.  
Figure 3: The four steps of a machine learning approach to predict age information of the unlabeled dataset.  
2.3.4. Predict and Explore the Age Information of Unlabeled Datasets  
Here, the \(agerate_{news}(n,g)\) values of age groups for a news article in the unlabeled dataset, \(NEWS_{\text{Unlabeled}}\), were obtained using the learned age predictor. Likewise, this study could deal with the unknown age information problem of anonymous commenters on the collected news articles; therefore, it enabled age difference analysis of the collected news articles, \(NEWS_{\text{Total}}\).  
The prediction results for the unlabeled dataset could not be evaluated by the MAE or RMSE because true target values were unavailable in the unlabeled dataset. Instead, this study explored the prediction results and compared them with the labeled and mixed datasets. Here, the mixed dataset was obtained by combining the labeled and unlabeled datasets. Figure 4 illustrates the three types of datasets.  
Specifically, the predicted \(agerate_{news}(n,g)\) values of the unlabeled news articles were visualized by drawing a histogram, which was compared with the distributions from the labeled and mixed datasets. Next, to investigate differences between these three datasets, this study measured and compared their descriptive statistics, i.e., normality, such as mean and standard deviation, and compared them between the three datasets.  
Additionally, to compare the three datasets, an investigation was conducted on sections. For this sectional investigation, the \(agerate_{news}(n,g)\) values were averaged for news articles belonging to a section \(S\), i.e., \(n\in NEWS_{\text{Section}}(S)\), which was defined as  
\[agerate_{section}(S,\ g)=\frac{1}{O(S)}{\sum_{n\in NEWS_{\text{Section}}(S)}} \,agerate_{new}(n,g), \tag{6}\]  
where \(O(S)=n(NEWS_{\text{Section}}(S))\). The statistic for the investigation with respect to subsections was given by  
\[agerate_{subsection}(s,\ g)=\frac{1}{P(s)}{\sum_{n\in NEWS_{\text{Subsection}}( s)}}\,agerate_{news}(n,g), \tag{7}\]  
where \(s\) is a subsection, \(NEWS_{\text{Subsection}}(s)\) is a set of news articles belonging to the subsection \(s\), i.e., \(n\in NEWS_{\text{Subsection}}(s)\), and \(P(s)=n(NEWS_{\text{Subsection}}(s))\).  
Then, using the \(agerate_{subsection}(s,g)\) values, the rank of age group \(g\) across all five age groups within subsection \(s\) was measured for the labeled and mixed datasets. This resulted in two metrics: \(rank_{labeled}(s,g)\) and \(rank_{mixed}(s,g)\). Subsequently, these two ranks for subsection \(s\) and age group \(g\) were considered as data points \((x,y)\) and displayed via a scatter diagram to investigate the difference between the labeled and mixed datasets.  
Figure 4: An illustration of how to obtain the mixed dataset.