# Uncertainty Quantification for MLP-Mixer Using Bayesian Deep Learning
## 3 Experiments and Results
With the availability of other mixer variants, we are optimistic that by combining them with BDL, mixer models can effectively compete with state-of-the-art approaches, even on small to medium-sized datasets. These results \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Mean Class Confidence \& Standard**} & \multicolumn{3}{c}{**Classes**} & \multicolumn{3}{c}{**Accuracy of Model**} \\ \cline{3-6}  & & **Deviation** & **Normal** & **Benign** & **Malignant** & **Base Model** & **Sampling** \\ \hline \multirow{2}{*}{Custom CNN + MC-Dropout} & Mean & 0.9192 & 0.9178 & 0.9569 & \multirow{2}{*}{0.7264} & \multirow{2}{*}{0.7179} \\  & SD & 0.1481 & 0.1217 & 0.0570 & & \\ \hline \multirow{2}{*}{Custom CNN + VI} & Mean & 0.8927 & 0.9011 & 0.8921 & \multirow{2}{*}{0.7380} & \multirow{2}{*}{0.7778} \\  & SD & 0.1511 & 0.1264 & 0.1363 & & \\ \hline \multirow{2}{*}{Inception + MC-Dropout} & Mean & 0.9019 & 0.9034 & 0.9383 & \multirow{2}{*}{0.7777} & \multirow{2}{*}{0.7692} \\  & SD & 0.1511 & 0.1455 & 0.1418 & & \\ \hline \multirow{2}{*}{Inception + VI} & Mean & 0.8882 & 0.8223 & 0.8279 & \multirow{2}{*}{0.7521} & \multirow{2}{*}{0.7435} \\  & SD & 0.1411 & 0.1739 & 0.1642 & & \\ \hline \multirow{2}{*}{DenseNet + MC-Dropout} & Mean & 0.9337 & 0.9245 & 0.9330 & \multirow{2}{*}{0.8290} & \multirow{2}{*}{0.8547} \\  & SD & 0.1151 & 0.0993 & 0.1078 & & \\ \hline \multirow{2}{*}{DenseNet + VI} & Mean & 0.9061 & 0.8418 & 0.8801 & \multirow{2}{*}{0.7692} & \multirow{2}{*}{0.7607} \\  & SD & 0.1447 & 0.1685 & 0.1327 & & \\ \hline \multirow{2}{*}{ResNet + MC-Dropout} & Mean & 0.8951 & 0.7149 & 0.8194 & \multirow{2}{*}{0.5299} & \multirow{2}{*}{0.7009} \\  & SD & 0.1420 & 0.1812 & 0.1466 & & \\ \hline \multirow{2}{*}{ResNet + VI} & Mean & 0.8313 & 0.7645 & 0.7947 & \multirow{2}{*}{0.6324} & \multirow{2}{*}{0.7692} \\  & SD & 0.1299 & 0.1451 & 0.1578 & & \\ \hline \multirow{2}{*}{MLP-Mixer + MC-Dropout} & Mean & 0.7566 & 0.7925 & 0.7880 & \multirow{2}{*}{0.6239} & \multirow{2}{*}{0.6923} \\  & SD & 0.2068 & 0.2069 & & \\ \hline \multirow{2}{*}{MLP-Mixer + VI} & Mean & 0.6598 & 0.6795 & 0.7417 & \multirow{2}{*}{0.5384} & \multirow{2}{*}{0.6325} \\  & SD & 0.2188 & 0.1467 & 0.1803 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of uncertainty quantification for different deep learning models used for the breast cancer dataset. offer promising directions for future research and highlight the potential of MLP-Mixers with BDL for practical applications in various domains. Figures 5 and 6 display a few examples of uncertainty quantification for the ALL dataset using the MC-Dropout approach. To accurately quantify the uncertainty of the predicted classes, 1000 samples were taken for each example. It should be noted that these image examples were randomly selected, which means that image (A) in Figure 5 is different from (A) in Figure 6, and similarly for (B) and (C). The (A) in both Figures 5 and 6 represents an accurately classified example with very low uncertainty (high confidence). We observed that when making predictions with low uncertainty, the mean for the true class was very close to 1.0, while the mean for other classes was close to 0.0. In addition, the standard deviation was very low for both true and false classes. Image (B) in both Figures 5 and 6 depicts a truly predicted class with moderately high uncertainty. Interestingly, the CNN model tended to have a curve peak near both ends of the scale, while the MLP-Mixer behaved very differently, with the curve peak at any point on the scale. Additionally, in general, the MLP-Mixer demonstrated higher uncertainty compared to CNN models, which is reflected in the results from Tables 1 and 2. Image (C) in both Figures 5 and 6 represents a misclassified category. In Figure 5C, even though the class \"early Pre-B\" is not the actual label for the associated image, it has a peak close to 1.0.