# Fast Minimum Error Entropy for Linear Regression
## 4 Experiments
Across all five experimental groups, FMEE consistently demonstrates a remarkable reduction in time consumption, consistently amounting to less than 1% of MEE's time expenditure. Moreover, in accordance with theoretical predictions, the computational cost of MEE exhibits quadratic growth relative to the sample size, whereas FMEE's time overhead scales linearly with the sample size. Table 5 conducts a comparative evaluation of the mean squared error (MSE) between MEE and FMEE in the context of non-Gaussian noise. Generally, the disparity between the MSE values of FMEE and MEE is relatively minor. Notably, FMEE outperforms MEE when the sample size is 100 or 400, while MEE exhibits superior performance for sample sizes of 200, 300, and 500. Additionally, FMEE attains the optimal MSE across all sample sizes, except for \(n=100\). Furthermore, it is observed that the MSE values for non-Gaussian noise, as depicted in Table 5, span a broader range compared to those for Gaussian noise, indicating greater variability in results for both MEE and FMEE. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample Size**} & \multicolumn{2}{c}{**Average Running Time**} & \multicolumn{2}{c}{**Optimal Running Time**} \\ \cline{2-5}  & **MEE** & **FMEE** & **MEE** & **FMEE** \\ \hline
100 & 107.96 & 0.0413 & 85.24 & 0.0156 \\
200 & 348.66 & 0.0635 & 270.26 & 0.0312 \\
300 & 800.50 & 0.0819 & 727.45 & 0.0468 \\
400 & 1431.34 & 0.1027 & 1274.87 & 0.0624 \\
500 & 2179.33 & 0.1178 & 1952.27 & 0.0624 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The running time of MEE and FMEE for non-Gaussian noise. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample Size**} & \multicolumn{2}{c}{**Average MSE**} & \multicolumn{2}{c}{**Optimal MSE**} \\ \cline{2-5}  & **MEE** & **FMEE** & **MEE** & **FMEE** \\ \hline
100 & 0.9108 & 1.4027 & 0.5697 & 0.6542 \\
200 & 0.9311 & 1.0528 & 0.6295 & 0.7258 \\
300 & 0.9573 & 1.0190 & 0.7600 & 0.7462 \\
400 & 0.9696 & 0.9769 & 0.8024 & 0.7588 \\
500 & 0.9604 & 0.9938 & 0.8024 & 0.8302 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The mean squared error of MEE and FMEE for Gaussian noise. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample Size**} & \multicolumn{2}{c}{**Average Iteration Number**} & \multicolumn{2}{c}{**Optimal Iteration Number**} \\ \cline{2-5}  & **MEE** & **FMEE** & **MEE** & **FMEE** \\ \hline
100 & 797.01 & 38.21 & 592 & 6 \\
200 & 697.09 & 38.29 & 592 & 7 \\
300 & 656.61 & 36.88 & 542 & 7 \\
400 & 650.03 & 40.67 & 571 & 9 \\
500 & 637.03 & 36.17 & 586 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of iterations of MEE and FMEE for Gaussian noise. Table 6 compares the number of iterations required for convergence between MEE and FMEE in the context of non-Gaussian noise. FMEE consistently demonstrates faster convergence compared to MEE. Furthermore, it is observed that the iteration count of MEE decreases as the sample size increases. In contrast, the iteration count of FMEE remains relatively stable despite variations in sample size. Based on the findings presented in Tables 1-6, it is evident that FMEE consistently yields comparable outcomes to MEE, albeit with significantly reduced time consumption and iteration counts. Notably, FMEE stands out for its remarkable efficiency, being approximately 1000 times faster than MEE and achieving convergence within approximately 0.1 s for 500 instances. Given its linear time complexity of \(O(n)\), FMEE holds considerable promise for deployment in real-time scenarios characterized by non-Gaussian noise. Subsequently, we embark on practical experimentation utilizing transformer characteristic data to forecast distribution network failures. The transformers are categorized into two groups based on their geographical location within distinct levels of urban activity within a specific city in northwest China.