## Experimental Results
### Overall Performance of SaSLM
#### 6.2.2 Performance for Bundle Sets  
We further ran experiments on item bundles. We analyzed the experimental results on YouShu and NetEase. Since the two datasets were originally constructed for BR, there are also some differences worth mentioning: (1) both Youshu and NetEase contain implicit feedback only; (2) the sets in both datasets contain variable sizes of items; (3) the sets in both datasets were not randomly constructed. Instead, they were constructed for a certain purpose: interaction with multiple users.  
Based on these difference, we added BGCN and removed ESARM to/from the comparison. Although, as mentioned in [5], ESARM can be extended to variable-length sets, it has certain implementation ambiguity. ESARM learns personalized weights for each extremal subset. However, for sets with variable length, the number of extremal subsets is undetermined. Therefore, it is not clear how to align the weights to the extremal scores. On the other hand, since the sets in YouShu and NetEase relate to multiple users, the  
\begin{table}
\begin{tabular}{l l r r r r} \hline \hline  & \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Set-Level**} & \multicolumn{2}{c}{**Item-Level**} \\ \cline{3-6}  & & **RMSE** & \(p\)**-Value** & **RMSE** & \(p\)**-Value** \\ \hline \multirow{8}{*}{**RealSet-Explicit**} & MFSet & 0.6340 & – & 0.9369 & – \\  & BCF & 0.6285 & – & 0.9296 & – \\ \cline{2-6}  & ARM-MF & 0.6294 & 0.2633 & 0.9274 & 0.0 \\  & VOARM-MF & 0.6333 & 0.4071 & 0.9152 & \(8.3\times 10^{-69}\) \\  & ESARM-MF & **0.6268** & 0.2230 & 0.9240 & \(6.6\times 10^{-54}\) \\  & SaSLM-MF & 0.6316 & – & **0.9103** & – \\ \cline{2-6}  & ARM-NCF & 0.6326 & 0.6439 & 0.9427 & 0.0 \\  & VOARM-NCF & 0.6343 & 0.5771 & 0.9325 & 0.0 \\  & ESARM-NCF & 0.6340 & 0.4569 & 0.9246 & 0.0004 \\  & SaSLM-NCF & 0.6336 & – & 0.9233 & – \\ \hline \multirow{8}{*}{**RealSet-Implicit**} & MFSet & 0.3967 & – & 0.4841 & – \\  & BCF & 0.3970 & – & 0.4795 & – \\ \cline{2-6}  & ARM-MF & 0.3973 & \(9.8\times 10^{-6}\) & 0.4810 & 0.0 \\  & VOARM-MF & **0.3964** & \(1.8\times 10^{-32}\) & 0.4750 & 0.0 \\  & ESARM-MF & 0.3981 & \(4.5\times 10^{-26}\) & 0.4784 & 0.0 \\  & SaSLM-MF & 0.4001 & – & **0.4697** & – \\ \cline{2-6}  & ARM-NCF & 0.4144 & \({}^{\blacktriangle}\) & \(2.9\times 10^{-14}\) & 0.5111 & 0.0 \\  & VOARM-NCF & 0.4090 & \(4.9\times 10^{-15}\) & 0.4934 & \(6.6\times 10^{-40}\) \\  & ESARM-NCF & 0.4058 & \({}^{\blacktriangle}\) & \(3.4\times 10^{-12}\) & 0.4793 & 0.0 \\  & SaSLM-NCF & 0.3977 & – & 0.4702 & – \\ \hline \hline \end{tabular} We show the best and second best results in **boldface** and underlined text. Statistical significance of pairwise differences in ARM, VOARM, and ESARM over SaSLM were determined by a \(t\)-test. \({}^{\blacktriangle}\) indicates the RMSE is significantly higher than that of SaSLM, and \({}^{\blacktriangledown}\) indicates the RMSE is significantly lower than that of SaSLM. If the \(p\)-value is lower than 0.01, it is considered significant. The \(p\)-value is also reported in the table to show the degree of significance. Note that the significant test was conducted using MF or NCF, respectively.  
\end{table}
Table 4: Performance of set-rating prediction with fixed-size setsuser-bundle graph can be constructed. Therefore, we implemented BGCN by propagating over the user-bundle graph.  
We report the results in Table 5. The best performance in item-rating prediction of both datasets was also achieved by SaSLM. Compared with RealSet, the baseline methods had better results in set-rating prediction, possibly due to the collaborative filtering among user-set interactions. Similarly, VOARM generally fit the set ratings well, since it considers the item rating diversity during rating aggregation. ARM and SaSLM had similar performances, both with MF and with NCF. While their performances in set-rating prediction were the same, SaSLM performed slightly better than ARM in item-rating prediction.