## 3 Results  
We downloaded the HABS-HD data from [10]; these data are available to the global scientific community to foster a more advanced understanding of the biological, social, cultural, and environmental factors associated with MCI and AD. The HABS-HD data used here contained 1328 normal controls and 377 MCIs and ADs (116 ADs and 261 MCIs). An imbalance occurred in this classification (class imbalance index = 0.31 according to the formula \(I=K*\sum_{i=1}^{K}(n_{i}-1/K)^{2}\), where \(K\) is the number of classes, and \(n_{i}\) is the number of instances of class \(i\)) because the MCI and AD group had a very low proportion in the training data compared to the normal control group. Moreover, the MCI and AD group had significantly more males (\(p\) = 8.95 \(\times\) 10\({}^{-7}\) < 0.001) and significantly fewer years of education (\(p\) = 2.60 \(\times\) 10\({}^{-7}\) < 0.001) than the normal control group. There was no significant difference in age between the two groups (\(p\) = 0.002 > 0.001). Detailed demographic characteristics of the cohort were presented in [10]. The following seventeen blood marker variables were chosen to predict the status of prevalent MCI and AD: CRP, FABP3, IL_10, IL_6, Ab40, Ab42, Tau, NFL, PPY, sICAM_1, sVCAM_1, TNF_alpha, GLP_1, Glucagon, PYY, Insulin, and HOMA_IR (Table 2). Age, Gender, Hispanic (Hispanic or not), and Edu (years of education) were added as covariates [9; 11; 14; 21]. We combined SLURM commands and R scripts to compare the computational time for hyperparameter tuning under different numbers of cores for a single node in Lonestar6 (Figure 1). The computational time for hyperparameter tuning for imbalanced data was inversely proportional to the number of cores for a single node (Figure 2a). For a single node, when we increased the number of cores from 1 to 128, the computational time was reduced but not linearly (Figure 2a). There was an overhead that reduced the efficiency, and not all of the tasks could be parallelized. The calculations of speedup vs. number of cores followed Amdahl's Law at a parallel proportion of 99% (Figure 2b). The computational time initially spent for the hyperparameter tuning without using high-performance computing \begin{table}
\begin{tabular}{c l c c} \hline \hline
**Variable Name** & **Description** & **Average Value** & **Standard Deviation** \\ \hline CRP & C-reactive protein (CRP) & 41,567,738 & 67,325,201 \\ FABP3 & Fatty acid-binding & 4953.23 & 2611.45 \\  & proteins (FABPs) & & \\ GLP\_1 & Glucagon-like & 1.07 & 2.09 \\  & peptide-1 (GLP-1) & & \\ Glucagon & Glucagon & 49.46 & 49.98 \\ IL\_6 & Human interleukin-6 (IL-6) & 1.85 & 19.63 \\ Insulin & Insulin & 233.35 & 287.24 \\ PPY & Pancreatic polypeptide (PPY) & 400.87 & 491.56 \\ PYY & Peptide YY (PYY), also known & & \\  & as peptide tyrosine tyrosine & 35.46 & 38.33 \\ sICAM\_1 & Interellular adhesion & & \\  & molecule 1 (ICAM-1/CD54) & & 2,354,989 & 2,759,979 \\ sVCAM\_1 & Vascular cell adhesion & & \\  & molecule 1 (VCAM-1/CD106) & & 3,681,600 & 4,361,946 \\ TNF\_alpha & Human tumor necrosis factor & & 3.57 & 15.14 \\  & alpha (TNF-alpha) & & \\ Ab40 & A940 is a 40-amino & & 244.08 & 78.38 \\  & acid proteolytic & & \\ Ab42 & A942 is a 42-amino & & 11.7 & 3.71 \\  & acid proteolytic & & 2.38 & 1.17 \\  & NFL & Neurofilament light & 18.47 & 14.08 \\ IL\_10 & Human interleukin-10 & & 0.42 & 0.64 \\ HOMA\_IR & Homeostatic model assessment & & 1.9 & 2.92 \\  & for insulin resistance & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description for the 17 variables. was 125.98 h. With 128 cores paralleled, the computational time decreased by up to 98.2% to 2.26 h. Measurement of the execution time for parallel SVM hyperparameter tuning was undertaken with the Sys.time() function in R (v4.1.2) by taking the difference between the times at the start and the end of the code chunk of the parallel SVM hyperparameter tuning. We used the grid search method to find the optimal hyperparameters (gamma = 0.02, cost = 0.25, class.weight = [0.79, 0.21]).