## 7 Results and Discussion
### Confidence Measure Results  
To show that the estimated probabilities of _yes_-answers actually resemble the true probabilities, a rough visualization is made for the activities in Figure 8 and for the environments in Figure 9. In the figures, all the answers from all users are sorted by the estimated probability, and the results are plotted using a circle if the user answer was _yes_ and with a cross in the case of a _no_ answer. To see if the prediction of probability is approximately working, we can then zoom into some probability level and see if the distribution between the circle (_yes_)) values agrees with the y-axis number. The lower box of Figure 8 shows an example where the predicted probability level of our model is 0.35 and the actual amount of yes answers in the data is 32%. Respectively, the higher box depicts a situation  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{true}\backslash\mathbf{decision}\) & **Off**. & **Nat**. & **Str**. & **Home** & **Res.** \\ \hline \(\mathbf{Off}.\) & \(76\) & \(0\) & \(2\) & \(11\) & \(11\) \\ \(\mathbf{Nat}.\) & \(0\) & \(55\) & \(35\) & \(5\) & \(5\) \\ \(\mathbf{Str}.\) & \(3\) & \(8\) & \(78\) & \(0\) & \(11\) \\ \(\mathbf{Home}\) & \(3\) & \(1\) & \(17\) & \(65\) & \(14\) \\ \(\mathbf{Res}.\) & \(11\) & \(0\) & \(30\) & \(0\) & \(59\) \\ \hline \hline \end{tabular}
\end{table}
Table 11: Confusion matrix of five environment classes _office_, _nature_, _street/road_, _home_ and _restaurant/pub/cafe_ before adaptation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{true}\backslash\mathbf{decision}\) & **Off**. & **Nat**. & **Str**. & **Home** & **Res.** \\ \hline \(\mathbf{Off}.\) & \(81\) & \(0\) & \(1\) & \(6\) & \(13\) \\ \(\mathbf{Nat}.\) & \(0\) & \(60\) & \(20\) & \(5\) & \(15\) \\ \(\mathbf{Str}.\) & \(3\) & \(5\) & \(73\) & \(5\) & \(14\) \\ \(\mathbf{Home}\) & \(3\) & \(1\) & \(9\) & \(74\) & \(13\) \\ \(\mathbf{Res}.\) & \(11\) & \(0\) & \(25\) & \(0\) & \(64\) \\ \hline \hline \end{tabular}
\end{table}
Table 12: Confusion matrix of five environment classes _office_, _nature_, _street/road_, _home_ and _restaurant/pub/cafe_ after adaptation.  
where our model predicts a proportion of yes answers to be 0.88, whereas the actual proportion of yes labeled samples in the data is 87%. This approximation shows that the estimation is working very well for activities, however, for environments (Figure 9) there are more differences in predicted probability compared to the estimate calculated using yes and no answers.  
To analyze the result more in detail, we also show the limits \(t_{l},t_{u}\) around the mean  
\[P(t_{l}\leq\theta<t_{u})=0.95, \tag{21}\]  
with \(\theta\sim Bin(N(yes)+N(no),p_{m})\) for each bin to see how the samples would deviate with perfectly known \(p_{m}\). The limits are shown in Figure 10 for the activities and Figure 11 for the environments,  
Figure 8: Predicted _yes_-probability for each sample in the sorted activities data. The small bar plots tell how many yes and no answers there are inside the two small rectangular areas.  
Figure 9: Predicted _yes_-probability for each sample in the sorted environment data. The small bar plots tell how many yes and no answers there are inside the two small rectangular areas.  
where the data is divided into 10 boxes having the middle points \(p_{m}=0.05\ldots 0.95\). The height of each bin is the number of yes answers satisfying \(|p_{m}-P_{yes|\mathbf{L}}|<0.05\). This result shows that for the activities the estimated confidence measure is consistent. However, for the environments the confidence measure is slightly optimistic.