# Fast Minimum Error Entropy for Linear Regression
## 4 Experiments
Initially, our attention is directed towards a subset of 1265 transformers situated within a smaller, less densely populated area of the aforementioned city. We undertake a random partitioning of this dataset into two segments: a training set comprising 80% of the data, totaling 1012 instances, and a verification set encompassing the remaining 20%, comprising 253 instances. To be more specific, the transformer dataset comprises various characteristic variables, involving the standardized heavy overload duration, maximum active load ratio, average active load ratio, mean three-phase unbalance, standardized heavy three-phase unbalance duration and so forth. We conduct a comparative analysis, pitting our proposed FMEE against three established baseline methodologies: logistic regression, neural network, and support vector machine. The dataset comprises 1265 transformer characteristic variables associated with substantial load levels, undergoing 30 rounds of random partitioning. Subsequently, each randomly divided dataset is subjected to four distinct algorithms. The predictive efficacy of these algorithms on the verification set is assessed based on F-measure and error rate metrics. Figure 1 depicts the F-measure evaluations stemming from 30 prediction instances conducted by four distinct algorithms. Notably, each evaluation involves consistent partitioning of the dataset across the four algorithms. A discernible trend emerges wherein all algorithms yield F-measure values surpassing 0.8. Notably, our proposed FMEE ex \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 & 782.88 & 34.33 & 618 & 8 \\
200 & 689.67 & 35.72 & 563 & 9 \\
300 & 644.95 & 36.72 & 584 & 10 \\
400 & 648.70 & 37.55 & 580 & 12 \\
500 & 633.25 & 35.35 & 571 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The number of iterations 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 & 1.0844 & 0.9604 & 0.1584 & 0.1630 \\
200 & 0.8485 & 1.1554 & 0.2654 & 0.2607 \\
300 & 0.9110 & 1.2314 & 0.3140 & 0.2659 \\
400 & 1.1037 & 1.0550 & 0.3672 & 0.2891 \\
500 & 0.9536 & 1.0491 & 0.4995 & 0.4668 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The mean squared error of MEE and FMEE for non-Gaussian noise. hibits the most promising performance, boasting an average F-measure of 0.904, thereby outshining the other three baseline methodologies by a significant margin. To facilitate a comprehensive comparison among the four algorithms, Figure 2 depicts the error rate and F-measure of fault outage prediction results in the form of line and box charts. Notably, FMEE emerges as a frontrunner, showcasing a substantial advantage over the sophisticated support vector machine in terms of error rate. Specifically, our FMEE achieves an average error rate of 9.1%, surpassing the neural network, logistic regression, and support vector machine by margins of 0.3%, 4.2%, and 4.3%, respectively. These findings underscore the clear superiority of our proposed FMEE methodology. Figure 1: The boxplot of F-measure among four algorithms for failure outage prediction results. Figure 2: The boxplot of error rate among four algorithms for failure outage prediction results. Furthermore, we extend our experimentation to a more densely populated urban region within the northwest Chinese city. Figure 3 illustrates the F-measure evaluations derived from 30 independent tests conducted across the four comparative algorithms. On a comprehensive scale, our proposed FMEE attains an F-measure of 0.891, surpassing baseline methodologies such as neural networks, logistic regression, and support vector machines by margins of 0.013, 0.023, and 0.028, respectively.