# A Piecewise Linear Regression Model Ensemble for Large-Scale Curve Fitting
## 7 Conclusions and Future Work  
In the current digital era, the exponential growth of data across various sectors presents unprecedented opportunities for insights and discoveries. However, handling large-scale datasets requires robust and scalable methods capable of fitting reliable models to extract meaningful knowledge. Traditional learning algorithms often struggle with large-scale data, as they are typically designed to run on single-core processors, accessing the entire input dataset. In this paper, some ensemble methods have been tested to obtain a continuous piecewise linear regression model from very large datasets based on the learning algorithm of the LHM. Additionally, this paper features a thorough analysis of results, wherein the mean squared error (MSE) is decomposed into its constituent components of bias and variance. This analysis offers valuable insights into the performance of the proposed ensemble meth \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**PR1 (Time (s))**} & \multicolumn{3}{c}{**PR2 (Time (s))**} & \multicolumn{3}{c}{**PR3 (Time (s))**} & \multicolumn{3}{c}{**PR4 (Time (s))**} \\ \hline  & \(M\) & \(t_{sub}\) & \(t_{sc}\) & \(t_{tot}\) & \(t_{sub}\) & \(t_{sc}\) & \(t_{tot}\) & \(t_{sub}\) & \(t_{sc}\) & \(t_{tot}\) & \(t_{sub}\) & \(t_{sc}\) & \(t_{tot}\) \\ \hline MS & 2 & 18.55 & 3.44 & 21.99 & 16.38 & 3.09 & 19.47 & 22.34 & 6.83 & 29.17 & 33.39 & 9.56 & 42.95 \\  & 5 & 54.87 & 3.54 & 58.41 & 46.87 & 3.18 & 50.05 & 61.54 & 6.83 & 68.37 & 95.32 & 9.57 & 104.89 \\  & 10 & 138.56 & 3.55 & 142.11 & 117.97 & 3.16 & 121.13 & 151.43 & 6.82 & 158.26 & 224.60 & 9.51 & 234.11 \\  & 20 & 283.71 & 3.58 & 287.28 & 245.99 & 3.18 & 249.17 & 311.64 & 6.74 & 318.39 & 455.19 & 9.42 & 464.61 \\  & 50 & 788.09 & 3.58 & 791.67 & 662.48 & 3.23 & 665.71 & 797.61 & 6.79 & 804.40 & 1156.44 & 9.52 & 1165.95 \\ \hline MC1 & 2 & 18.55 & 0.00 & 18.55 & 16.38 & 0.00 & 16.38 & 22.34 & 0.00 & 22.34 & 33.39 & 0.00 & 33.39 \\  & 5 & 54.87 & 0.00 & 54.87 & 46.87 & 0.00 & 46.87 & 61.54 & 0.00 & 61.54 & 95.32 & 0.00 & 95.32 \\  & 10 & 138.56 & 0.00 & 138.57 & 117.97 & 0.00 & 117.97 & 151.43 & 0.00 & 151.44 & 224.60 & 0.00 & 224.60 \\  & 20 & 283.71 & 0.01 & 283.72 & 245.99 & 0.01 & 246.00 & 311.64 & 0.01 & 311.65 & 455.19 & 0.01 & 455.20 \\  & 50 & 788.09 & 0.02 & 788.11 & 662.48 & 0.02 & 662.49 & 797.61 & 0.02 & 797.62 & 1156.44 & 0.02 & 1156.45 \\ \hline MC2 & 2 & 18.55 & 8.61 & 27.15 & 16.38 & 7.67 & 24.05 & 22.34 & 17.27 & 39.61 & 33.39 & 22.55 & 55.94 \\  & 5 & 54.87 & 11.30 & 66.17 & 46.87 & 10.47 & 57.35 & 61.54 & 23.19 & 84.72 & 95.32 & 28.90 & 124.22 \\  & 10 & 138.56 & 13.51 & 152.07 & 117.97 & 117.99 & 129.75 & 151.43 & 27.04 & 178.47 & 224.60 & 31.94 & 256.54 \\  & 20 & 283.71 & 10.48 & 294.19 & 245.99 & 8.65 & 254.64 & 311.64 & 21.24 & 332.89 & 455.19 & 26.53 & 481.72 \\  & 50 & 788.09 & 18.35 & 806.44 & 662.48 & 15.42 & 677.90 & 797.61 & 33.59 & 831.20 & 1156.44 & 44.88 & 1201.32 \\ \hline MC3 & 2 & 18.55 & 29.12 & 47.66 & 16.38 & 26.79 & 43.17 & 22.34 & 53.24 & 75.58 & 33.39 & 88.24 & 121.63 \\  & 5 & 54.87 & 31.03 & 85.90 & 46.87 & 27.43 & 74.30 & 61.54 & 53.33 & 114.87 & 95.32 & 88.01 & 183.34 \\  & 10 & 138.56 & 32.21 & 170.77 & 117.97 & 27.64 & 145.61 & 151.43 & 52.19 & 203.62 & 224.60 & 84.47 & 309.07 \\  & 20 & 283.71 & 21.29 & 304.99 & 245.99 & 17.24 & 263.23 & 311.64 & 35.61 & 347.26 & 455.19 & 60.57 & 515.76 \\  & 50 & 788.09 & 31.87 & 819.96 & 662.48 & 27.52 & 689.99 & 797.61 & 50.69 & 848.30 & 1156.44 & 82.85 & 1239.29 \\ \hline RA & - & - & - & **114.87** & - & - & **83.82** & - & - & **147.19** & - & - & **180.37** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average CPU-time of the proposed methods with different values of \(M\) and \(n=1\) M, applied to all the problems (calculated from 30 replications). \(t_{sub}\) represents the total calculation time of the sub-models. \(t_{sc}\) represents the execution time of the model selection or combination method. This time includes a final OLS in the case of MS, MC2, and MC3.