# Enhancing Neural Network Interpretability Through Deep Prior-Guided Expected Gradients
## 4 Experiments
### Results
#### 4.3.1 Evaluation on ImageNet
Figure 4: In the original images of agama and American egret (**a**), the prediction results of ResNet50 are explained using expected gradients (**b**), DeepBGMM-EG (**c**) and DeepMGM-EG (**d**) methods, presenting the corresponding feature attribution maps. Figure 5: In the original images of agama and American egret (**a**), the prediction results of VGG16 are explained using expected gradients (**b**), DeepBGMM-EG (**c**) and DeepMGM-EG (**d**) methods, presenting the corresponding feature attribution maps. Similarly, Table 2 reports the comparison for VGG16. DeepBGMM-EG outperformed other methods in KPM, KAM, RPM, RNM, and RAM, demonstrating its strong capability in handling feature importance and recovery, which enhanced model interpretability and reliability. Although EG and LIFT performed comparably on the KNM metric, DeepBGMM-EG exhibited superior performance on most metrics. DeepMGM-EG also performed well but was slightly less effective than DeepBGMM-EG on KPM and KAM. These results indicate that DeepBGMM-EG provides more comprehensive and accurate feature evaluations, contributing to improved interpretability in deep learning models. In general, DeepBGMM-EG's performance in VGG16 further validates its potential as an effective interpretability method, as DeepBGMM-EG demonstrates a stronger alignment with the model's behavior. To rigorously validate the statistical significance of improvements, we conducted a bootstrap resampling experiment with 10,000 iterations. The standard deviation for EG was set to \(\theta=0.1\) based on its original paper's random baseline fluctuations, while we conservatively assumed \(\theta=0.2\) for DeepBGMM-EG despite actual measurements suggesting lower variance. Using a one-sided hypothesis test with the test statistic shown in Equations (22) and 23, respectively. \[H0:KPM_{DeepBGMM-EG}<=KPM_{EG};H1:KPM_{DeepBGMM-EG}>KPM_{EG} \tag{22}\]  
\[\delta=KPM_{DeepBGMM-EG}-KPM_{EG} \tag{23}\]  
we obtained a statistically significant result (\(p<0.001\)) with 95% confidence interval \([0.026,0.062]\) via the percentile method. These quantitative validations, combined with the visual explanations in Figures 2-5 and metric comparisons in Tables 1 and 2, confirm that DeepBGMM-EG provides statistically reliable and human-aligned explanations. The method's ability to suppress background artifacts while emphasizing object-centric features--demonstrated by both attribution maps and rigorous bootstrap analysis--establishes it as a robust tool for in \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Method** & **KPM** & **KNM** & **KAM** & **RPM** & **RNM** & **RAM** \\ \hline EG & 1.0952 & \(-\)**1.1014** & **0.9653** & **1.2502** & \(-\)1.2558 & 1.4305 \\ LIFT & 1.1027 & \(-\)1.1283 & 0.9288 & 1.2120 & \(-\)**1.2316** & **1.4432** \\ DeepBGMM-EG & **1.1193** & \(-\)1.1279 & 0.9580 & 1.2224 & \(-\)1.2340 & 1.4361 \\ DeepMGM-EG & 1.1192 & \(-\)1.1283 & 0.9565 & 1.2217 & \(-\)1.2333 & 1.4342 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of different explanation methods (EG, DeepBGMM-EG, DeepMGM-EG, and LIFT) based on various metrics (KPM, KNM, KAM, RPM, RNM, RAM) for ResNet50 predictions. The dataset consists of 600 images selected from the ImageNet validation set, with 50 images per category from 12 categories. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Method** & **KPM** & **KNM** & **KAM** & **RPM** & **RNM** & **RAM** \\ \hline EG & 1.2418 & \(-\)1.2390 & 1.0217 & 2.4655 & \(-\)2.4639 & 2.8490 \\ LIFT & 1.0055 & \(-\)**0.8827** & 0.9758 & **2.7043** & \(-\)2.6894 & 2.8403 \\ DeepBGMM-EG & **1.2603** & \(-\)1.2412 & **1.0244** & 2.3692 & \(-\)**2.3510** & 2.7601 \\ DeepMGM-EG & 1.2540 & \(-\)1.2416 & 1.0131 & 2.4678 & \(-\)2.4566 & **2.8758** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of different explanation methods (EG, DeepBGMM-EG, DeepMGM-EG, and LIFT) based on various metrics (KPM, KNM, KAM, RPM, RNM, RAM) for VGG16 predictions.