# DACSR: Decoupled-Aggregated End-to-End Calibrated Sequential Recommendation
## 6 Results and Analysis
### RQ4: Distribution Modification  
In this section, we answer the research question RQ4 about the effectiveness of the proposed distribution modification approaches. We proposed the modified distribution \(p_{d}(s)\) and \(p_{m}(s)\) to further improve the diversity and mitigate the imbalanced interest problem. These approaches are related to the diversity. Therefore, we adopted the ILD metric with Jaccard similarity to measure the diversity of the recommendation list:  
\[ILD(RL_{s})=\frac{2}{\mid RL_{s}\mid(\mid RL_{s}\mid-1)}\sum_{(i,j)\in RL_{s} )}(1-\frac{\mid Att_{i}\cap Att_{j}\mid}{\mid Att_{i}\cup Att_{j}\mid}) \tag{27}\]  
where \(Att_{i}\) is the item attribute set that the item \(i\) has, and \(RL_{s}\) is the generated recommendation list for sequence \(s\). The larger ILD value represents the higher diversity of the recommendation list. We set the factor \(\tau_{div}=0.5\) and 2 for the distribution \(p_{d}(s)\) and \(p_{m}(s)\), respectively. We first listed the performances of our DACSR model with the raw historical preference distribution (namely DACSR-\(p(s)\)) and the modified preference distribution for diversity (namely DACSR-\(p_{d}(s)\)) along with the original SASRec model in Table 6.  
On the two datasets, the diversity of our model is improved by sacrificing the calibration. For example, on the MI-1m dataset, the performances of \(ILD\)@10 are 0.7012 and 0.6654 for the normalized distribution \(p_{d}(s)\) and the original distribution \(p(s)\), respectively. However, the \(C_{KL}\)@10 increases from 1.0615 to 1.1347, which means the ability of calibration of our model is weakened. On the Tmall dataset, the performance comparisons are similar. This is because applying the normalized distribution amplifies the effect of item attributes \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Datasets** & **Models** & **ILD@10** & \(\mathbf{C_{KL}}\)@10 & **ILD@20** & \(\mathbf{C_{KL}}\)@20 \\ \hline \multirow{4}{*}{Ml-1m} & SASRec & 0.6499 & 1.2385 & 0.6677 & 0.8548 \\ \cline{2-6}  & DACSR-\(p(s)\) & 0.6654 & **1.0615** & 0.6789 & **0.7262** \\ \cline{2-6}  & DACSR-\(p_{d}(s)\) & **0.7012** & 1.1347 & **0.7123** & 0.7649 \\ \hline \multirow{4}{*}{Tmall} & SASRec & 0.7086 & 2.4871 & 0.7405 & 2.1092 \\ \cline{2-6}  & DACSR-\(p(s)\) & 0.6714 & **2.0114** & 0.7045 & **1.6240** \\ \cline{1-1} \cline{2-6}  & DACSR-\(p_{d}(s)\) & **0.7419** & 2.2662 & **0.7725** & 1.8412 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performances of calibration and diversity (best performances are marked in bold). that the user did not interacted in the behavior sequence. Though it does not largely affect the true distribution \(p(s)\), it deviates from the calibration to a certain degree. We observe that our DACSR model performed differently on the two datasets. On the MI-1m dataset, the diversity is higher for our DACSR model than the original SASRec model, while it is totally different on the Tmall dataset. On the Tmall dataset, our DACSR model achieves worse performance in terms of diversity (e.g., 0.6714 vs. 0.7086 of DACSR and SASRec model). It is possibly due to the difference between two datasets. On the MI-1m dataset, the coverage of item attributes is higher than the Tmall dataset. Users have more historical behaviors than the Tmall dataset. On the Tmall dataset, users always interacted with several types of items, so that the \(p(g\mid s)\) score of most attributes equals to 0. The limited interest areas resulted in less diversified recommendation lists under the calibration objective. We also investigate the imbalanced interest problem. We find that main interests are amplified on the Tmall dataset. As illustrated in Figure 5, the attribute \(A\) occupies the 80% of the sequence, while attribute \(B\) and \(C\) only account for the 20%. For such an imbalanced distribution, our DACSR model amplifies the major interest, as shown in Figure 5. The recommended list only contains items with attribute \(A\). This gives our model a negative impact in terms of diversity.