# Diffusion Model as a Base for Cold Item Recommendation
## 5 Result Analysis
### DM's Hyperparameter Effect (RQ2)  
**DM's Noise Schedule:** Here, we evaluate the performance of DMCIR with various values of \(\beta_{e}\) in Equation (2). Figure 4 plots the decay ratio of \(x_{0}\) in the forward process to \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Dataset** & **Metric** & **DONet** & **Heater** & **CVAR** & **CCFC** & **GME** & **DMCIR** & **DMCIR+** \\ \hline \multirow{8}{*}{CiteULike} & P@10 & 0.099 & 0.119 & 0.112 & 0.119 & 0.116 & 0.120 & **0.127** \\  & P@20 & 0.076 & 0.089 & 0.088 & 0.089 & 0.087 & 0.090 & **0.095** \\  & P@50 & 0.050 & 0.055 & 0.054 & 0.054 & 0.055 & 0.054 & **0.058** \\ \cline{2-9}  & R@10 & 0.213 & 0.256 & 0.251 & 0.273 & 0.248 & 0.263 & **0.278** \\  & R@20 & 0.325 & 0.372 & 0.376 & 0.389 & 0.361 & 0.379 & **0.401** \\  & R@50 & 0.506 & 0.554 & 0.557 & 0.557 & 0.532 & 0.549 & **0.581** \\ \cline{2-9}  & N@10 & 0.223 & 0.274 & 0.262 & 0.276 & 0.265 & 0.277 & **0.291** \\  & N@20 & 0.270 & 0.313 & 0.304 & 0.313 & 0.311 & 0.317 & **0.334** \\  & N@50 & 0.327 & 0.360 & 0.351 & 0.347 & 0.356 & 0.353 & **0.376** \\ \hline \multirow{8}{*}{ML25M} & P@10 & 0.282 & 0.328 & 0.281 & 0.287 & 0.231 & 0.309 & **0.330** \\  & P@20 & 0.236 & **0.270** & 0.237 & 0.232 & 0.186 & 0.255 & **0.270** \\  & P@50 & 0.168 & 0.184 & 0.168 & 0.157 & 0.127 & 0.176 & **0.185** \\ \cline{1-1} \cline{2-9}  & R@10 & 0.194 & 0.224 & 0.192 & 0.205 & 0.138 & 0.210 & **0.230** \\ \cline{1-1}  & R@20 & 0.301 & 0.343 & 0.301 & 0.301 & 0.207 & 0.332 & **0.346** \\ \cline{1-1}  & R@50 & 0.485 & 0.523 & 0.489 & 0.462 & 0.323 & 0.503 & **0.531** \\ \cline{1-1} \cline{2-9}  & N@10 & 0.404 & 0.466 & 0.399 & 0.418 & 0.332 & 0.436 & **0.471** \\ \cline{1-1}  & N@20 & 0.472 & 0.531 & 0.465 & 0.466 & 0.375 & 0.503 & **0.535** \\ \cline{1-1}  & N@50 & 0.590 & 0.636 & 0.588 & 0.562 & 0.455 & 0.618 & **0.645** \\ \hline \hline \end{tabular} Boldface type: the best performance. Underline: the second-best performance.  
\end{table} 
Table 4: Overall recommendation performance. timestep \(t\) (\(\sqrt{\bar{\alpha_{t}}}\) in Equation (3)) for different \(\beta_{e}\) values. As the value of \(\beta_{e}\) increases, the speed of the original signal decay also increases. Table 6 plots the performance of DMCIR with \(\beta_{e}\in\{0.02,0.03,0.04,0.05,0.06\}\). The other hyperparameters, the number of experts \(|E|\) and the maximum timestep \(T\) are fixed to 5 and 400, respectively. The average performance increases as \(\beta_{e}\) increases to 0.05. The performance starts to decrease at \(\beta_{e}=0.06\). This trend indicates that the original information available in the last part of the forward process affects the reconstruction accuracy. As shown \(\beta_{e}=0.02\) in Figure 4, when \(\beta_{e}\) is small, the signal-to-noise ratio (SNR) of the original information does not become zero at \(T\). As [PERSON] et al. (2017) pointed out, the remaining original information in the training phase makes the denoiser (predictor) try to seek the original information at \(x_{T}\), which is regarded as a pure Gaussian noise. Because we do not know collaborative embeddings of cold items, we set a pure Gaussian noise as \(x_{T}\) is in the inference phase. The performance drop at small \(\beta_{e}=0.02\) is caused because the denoiser considers a noise as information