## 3 Results
### Model Performance and Variable Importance  
During 600 epochs, the test set loss of WAD registered a steady fall from 23 to 13 (Figure 4). The accuracy results were 61%, 100%, and 75% for the minimal, moderate, and significant change groups, correspondingly (average 71%). With the minimal and moderate change groups being combined, the accuracy outcomes were 100% and 75% for the combined and significant groups, respectively (average 88%) (Table 2). Here, accuracy means \"accuracy for a class\", i.e., predicted observations over actual observations for a class, namely, 0, 1, or 2. This becomes specificity (for a class of \"0\") or sensitivity (for a class of \"1\") in the case of binary prediction. Average accuracy is a simple form of the F1 score. Based on reinforcement learning (neural architecture search), the optimal region of interest for predicting weight loss was identified as the entire cross-section above the diaphragm, as shown in Figure 5. As explained above, neural architecture search represents systematic selection for the width and height of the region of interest, which maximizes the performance of WAD. This study identified baseline HOMA2-B, insulin, and vitamin B12 as the most important predictors of BMI change over one year. The importance of a predictor was calculated by the performance gap between the model without its permutation and the model with its permutation (\"variable permutation importance\"). Here, permutation refers to randomly shuffling the values of a particular variable so that it no longer contributes to the model's prediction process. For example, the importance of HOMA2-B, 0.1255, indicates a performance difference between WD without its permutation and WD with its permutation. The permutation importance rankings of five predictors, HOMA2-B, insulin, vitamin B12, fast plasma glucose, alanine transaminase, and HOMA2-S, were similar in WD and RF, a popular machine learning model. Here, the terms WD and RF denote wide and deep learning and random forest, respectively (Table 3). \begin{table}
\begin{tabular}{l l} \hline
**Variables** & **Values (n = 45)** \\ \hline HOMA2-S (\%) & 45.9 (50.0) \\ \hline HOMA2-IR & 3.2 (1.5) \\ \hline HbA1c, \% & 6.3 (1.1) \\ \hline C-reactive protein, ng/mL & 5.2 (6.5) \\ \hline Uric acid, mg/dL & 6.2 (1.8) \\ \hline Total cholesterol, mg/dL & 176.0 (43.6) \\ \hline Triglyceride, mg/dL & 146.0 (63.3) \\ \hline High density lipoprotein cholesterol, mg/dL & 46.7 (10.4) \\ \hline Low density lipoprotein cholesterol, mg/dL & 106.7 (39.8) \\ \hline Iron, \(\mu\)g/dL & 86.7 (41.2) \\ \hline Vitamin B\({}_{12}\), pg/mL & 672.7 (274.0) \\ \hline Systolic blood pressure, mmHg & 142.1 (13.8) \\ \hline Hypertension, n (\%) & 33 (73) \\ \hline Type 2 diabetes, n (\%) & 16 (36) \\ \hline Dyslipidemia, n (\%) & 23 (51) \\ \hline Depression, n (\%) & 10 (22) \\ \hline \end{tabular} Values are given as mean \(\pm\) standard deviation.  
\end{table} 
Table 1: _Cont._Figure 4: Test set loss of wide and deep learning during 600 epochs. Legend: during 600 epochs, the test set loss of wide and deep learning registered a steady fall from 23 to 13. Figure 5: Optimal regions of interest based on reinforcement learning. Legend: analysis of abdominal CT images using reinforcement learning (neural architecture search) to identify the region of interest most associated with weight loss revealed that the entire cross-section at the above-diaphragm level was the most significant. \begin{table}
\begin{tabular}{l l l} \hline
**Accuracy** & **3-Class** & **2-Class** \\ \hline G1 & 0.61 & \\ G2 & 1.00 & 1.00 \\ G3 & 0.75 & 0.75 \\ \hline Total & 0.71 & 0.88 \\ \hline \end{tabular} Note: G1, minimal change group; G2, moderate change group; G3, significant change group.  
\end{table} 
Table 2: Model performance. Legend: The accuracy results were 61%, 100%, and 75% for the minimal, moderate, and significant change groups, correspondingly (average 71%).