# Diffusion Model as a Base for Cold Item Recommendation
## 5 Result Analysis
### DM's Hyperparameter Effect (RQ2)
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **Metric** & \(\beta_{e}=\textbf{0.02}\) & \(\beta_{e}=\textbf{0.03}\) & \(\beta_{e}=\textbf{0.04}\) & \(\beta_{e}=\textbf{0.05}\) & \(\beta_{e}=\textbf{0.06}\) \\ \hline \multirow{6}{*}{CiteULike} & P@10 & 0.118 & **0.120** & **0.120** & **0.120** & **0.120** \\  & P@20 & 0.089 & **0.090** & **0.090** & **0.090** & **0.090** \\  & P@50 & 0.054 & 0.054 & 0.054 & **0.055** & **0.055** \\ \cline{2-6}  & R@10 & 0.260 & **0.263** & **0.263** & **0.263** & 0.262 \\  & R@20 & 0.373 & 0.377 & **0.379** & **0.379** & 0.376 \\  & R@50 & 0.545 & 0.546 & 0.549 & **0.550** & 0.549 \\ \cline{2-6}  & N@10 & 0.272 & 0.275 & **0.277** & 0.275 & **0.277** \\  & N@20 & 0.312 & 0.314 & **0.317** & **0.317** & **0.317** \\  & N@50 & 0.351 & 0.352 & 0.353 & **0.355** & 0.354 \\ \hline \multirow{6}{*}{ML25M} & P@10 & **0.307** & 0.292 & 0.294 & 0.299 & 0.296 \\  & P@20 & **0.254** & 0.236 & 0.238 & 0.239 & 0.238 \\  & P@50 & 0.175 & 0.174 & **0.176** & **0.176** & **0.176** \\ \cline{1-1} \cline{2-6}  & R@10 & 0.209 & 0.226 & 0.229 & **0.231** & 0.229 \\ \cline{1-1}  & R@20 & 0.322 & 0.355 & **0.357** & **0.357** & 0.353 \\ \cline{1-1}  & R@50 & 0.499 & 0.497 & **0.503** & 0.501 & 0.499 \\ \cline{1-1} \cline{2-6}  & N@10 & 0.435 & 0.445 & 0.446 & **0.451** & 0.449 \\ \cline{1-1}  & N@20 & 0.501 & 0.523 & **0.526** & **0.526** & 0.522 \\ \cline{1-1}  & N@50 & 0.613 & 0.612 & **0.620** & 0.618 & 0.616 \\ \hline \hline \end{tabular} Boldface type: the best performance. Underline: the second-best performance.  
\end{table} 
Table 6: Performance of DMCIR with regard to the noise schedule. Figure 4: Original signal strength vs. timesteps. from \(x_{0}\). The phenomenon is mitigated as \(\beta_{e}\) increases, but when \(\beta_{e}\) is greater than 0.05, the available information of \(x_{0}\) in the last part of the forward process becomes too small. That also hinders the performance of the denoiser. It is important to determine the optimal value of \(\beta_{e}\). Based on our experimental result showing that \(\beta_{e}\in[0.04,0.05]\) yields consistently fair performance across datasets, we suggest 0.04 to 0.05 as a reasonable choice. **Maximum Timesteps:** For DM, an optimal value of the maximum timesteps \(T\) is critical. When the value of \(T\) is too small, although the training and inference costs are reduced, the noise scale applied to each timestep increases. That makes the denoising process difficult. On the other hand, when the value of \(T\) is too large, the denoising process becomes easier, resulting in increased computational costs. Figure 5 shows DMCIR's performance with the CiteULike ((a)) and ML25M ((b)) datasets to various \(T\in\{100,200,300,400,500,600\}\). We fixed the other parameters as \(\beta_{e}=0.05\) and \(|E|=5\). Generally, the recommendation performance increases as the value of \(T\) increases and reaches its peak at 300 and 400. After that, the performance starts to decline. This observation is caused by the extremely small noise size of the single timestep. The extremely small size of the noise is also difficult to predict accurately. Considering the performance and cost trade-off, the value of \(T\) as 300 or 400 is a good choice. **The Number of Experts in \(x_{0}\)-Predictor of DM:** The \(x_{0}\)-predictor of DMCIR adopts a Mixture-Of-Experts architecture to generate the first prediction \(\hat{x}_{0}^{(1)}\) in Equation (13), which is used for prediction guidance of DM. In Figure 6, we show the recommendation performance of DMCIR with CiteULike ((a)) and ML25M ((b)) datasets to various number  
Figure 5: Performance with regard to the maximum timestep \(T\). of experts \(|E|\in\{0,1,3,5,7\}\). \"\(|E|=0\)\" indicates that MoE in Figure 2 is removed. The other parameters were fixed as \(\beta_{e}=0.05\) and \(T=400\). In all datasets, the worst performance was observed when \"\(|E|=0\)\", indicating that MoE contributes to the recommendation performance.