## 5 Experiments
### Observation Time Window Study
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Types** & **Model Name** & **T (a)** & **HR@IP** & **HR@SP** & **HR@10P** & **HR@15P** & **NDCG@IP** & **NDCG@10P** & **NDCG@15P** & **MSE** \\ \hline \multirow{4}{*}{\begin{tabular}{c} Statistics -based \\ \end{tabular} } & 3 & 0.677 & 0.791 & **0.798** & **0.808** & 0.712 & 0.766 & 0.787 & 0.784 & 0.077 \\  & 2 & 0.656 & **0.776** & 0.777 & **0.787** & 0.700 & 0.748 & 0.773 & 0.769 & 0.083 \\  & num\_at\_T & 1 & 0.591 & 0.736 & 0.719 & 0.731 & 0.654 & 0.724 & 0.746 & 0.744 & 0.094 \\  & 0.5 & 0.484 & 0.586 & 0.554 & 0.570 & 0.613 & 0.674 & 0.701 & 0.703 & 0.109 \\ \hline \multirow{4}{*}{\begin{tabular}{c} Feature \\ -based \\ \end{tabular} } & 3 & 0.645 & 0.778 & 0.791 & 0.758 & 0.711 & 0.780 & 0.802 & 0.845 & 0.069 \\  & 2 & 0.581 & 0.753 & 0.778 & 0.737 & 0.666 & 0.769 & 0.757 & 0.839 & 0.072 \\  & 1 & 0.559 & 0.4723 & 0.754 & 0.695 & 0.669 & 0.754 & 0.797 & 0.820 & 0.078 \\ \cline{2-11}  & 0.5 & 0.484 & 0.676 & 0.709 & 0.633 & 0.642 & 0.719 & 0.777 & 0.798 & 0.087 \\ \cline{2-11}  & 3 & 0.707 & 0.786 & 0.785 & 0.757 & 0.761 & 0.800 & 0.825 & 0.853 & 0.062 \\  & 2 & 0.681 & 0.770 & 0.773 & 0.735 & 0.737 & 0.789 & 0.817 & 0.851 & 0.066 \\  & 1 & 0.640 & 0.728 & 0.747 & 0.689 & 0.742 & 0.789 & 0.837 & 0.849 & 0.069 \\  & 0.5 & 0.534 & 0.687 & 0.714 & **0.654** & 0.663 & 0.733 & 0.788 & 0.801 & 0.085 \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Deep \\ -learning \\ -based \\ \end{tabular} } & 3 & 0.699 & 0.771 & 0.712 & 0.728 & 0.740 & 0.793 & 0.818 & 0.844 & 0.067 \\  & 2 & 0.677 & 0.752 & 0.677 & 0.714 & 0.762 & 0.789 & 0.821 & 0.080 \\  & 1 & 0.613 & **0.743** & 0.617 & 0.668 & 0.692 & 0.757 & 0.809 & 0.820 & 0.081 \\  & 0.5 & 0.541 & 0.679 & 0.568 & 0.635 & 0.679 & 0.746 & 0.793 & 0.813 & 0.083 \\ \cline{2-11}  & 3 & 0.720 & 0.791 & 0.797 & 0.729 & 0.757 & 0.792 & 0.818 & 0.849 & 0.065 \\ \cline{2-11}  & 2 & 0.685 & 0.771 & **0.793** & 0.714 & 0.725 & 0.727 & 0.808 & 0.836 & 0.70 \\ \cline{2-11}  & \multirow{2}{*}{
\begin{tabular}{c} ExoFIA \\ -based \\ \end{tabular} } & 3 & 0.629 & 0.738 & 0.741 & 0.670 & 0.689 & 0.758 & 0.804 & 0.814 & 0.077 \\ \cline{2-11}  & 0.570 & 0.682 & 0.694 & 0.633 & 0.669 & 0.729 & 0.788 & 0.801 & 0.085 \\ \cline{2-11}  & 3 & **0.753** & **0.799** & 0.797 & 0.754 & **0.825** & **0.853** & **0.868** & **0.882** & **0.049** \\ \cline{2-11}  & 2 & **0.734** & 0.774 & 0.791 & 0.732 & **0.800** & **0.834** & **0.850** & **0.865** & **0.058** \\ \cline{2-11}  & 1 & **0.664** & 0.737 & **0.758** & 0.686 & **0.774** & **0.818** & **0.841** & **0.855** & **0.066** \\ \cline{2-11}  & 0.5 & **0.573** & **0.691** & **0.715** & 0.641 & **0.723** & **0.786** & **0.825** & **0.826** & **0.076** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Prediction performance within different observation times (T). The best result in each row is in boldface. cascades usually have a longer growth period, and thus, a longer observation time window can adequately capture the growth of its lifespan. Moreover, as the size of the observation time window increases, the cascade becomes saturated; thus, the prediction errors decline and ranking metrics ascend for all models (see Figure 16). Furthermore, the proposed ExoFIA performs better than these baselines under a variety of circumstances related to different windows, further validating the robustness of our model. We observe an interesting phenomenon in Figure 16b. Node_num_at_T has the worst performance when the observation time is 0.5 h, but its performance abruptly increases with the observation time and surpasses most models. For clarity, we only chose node_num_at_T and Feature-deep for illustration. In Table 10, we find that as the observation time increases, the _HR@k_ (with k varying from small to large) of node_num_at_T gradually exceeds the value of Feature-deep. As the observation time increases, saturation of the cascade is likely to occur, and node_num_at_T will become closer and closer to the final size of the cascade.