# Transfer Learning: Video Prediction and Spatiotemporal Urban Traffic Forecasting +
## 4 Experimental Results
### Estimation Results  
The average performance of each model was estimated by the rolling window technique for 10 weeks of data. Given that the first five days were reserved for the look-back interval and the rolling step was selected as one hour (\(l=12\)), we trained every model specification for 1560 data subsets  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hyperparameter** & **Symbol** & **Tested Values** & **Used in Models** \\ \hline Radii of spatial & \(r_{1}\), \(r_{2}\) & [0, 10, 20, 30] & SpX-lm, SpX-SVR, \\ neighborhoods & & & SpX-ARIMAX \\ Spatial inflation & _step_ & [0, 5] & SpX-lim, SpX-SVR, \\ Spatial weights & \(w\) & \(w_{e}\), \(w_{1/d}\) & SpX-lim, SpX-SVR, \\ Distance decay speed for \(w_{e}\) & \(\sigma^{2}\) & [10, 20] & GCNN \\ Cross-correlation threshold & \(\theta\) & [0.1, 0.2, 0.3] & SpVAR-cc \\ Order of autoregression and & \(p\), \(q\) & Hyndman and Khandakar’s & ARIMA, SpX-ARIMAX \\ moving average components & & algorithm [56] & VAR, SpVAR-tt, \\ Order of autoregression & \(p\) & [1, 3, 6] & SpVAR-cc \\ Look-back interval & \(L\) & [360, 720, 1440] & All models \\ \hline \hline \end{tabular}
\end{table}
Table 2: Hyperparameter overview.  
and obtained their short-term forecasts (\(h=3\)). Further, the optimal set of hyperparameters for every model specification was selected on the basis of the average one-step-ahead forecasting accuracy.  
Obtained forecasting accuracy metrics for the optimal set of hyperparameters are summarized in Table 3 (model specifications with highest forecasting accuracy are marked by bold).  
Table 3 provides average values of forecasting accuracy metrics, which could be misleading due to the significant heterogeneity of results over spatial and temporal dimensions. Figure 5 represents spatial and temporal kernel densities of MAE values for three model specifications: ARIMA, SpX-ARIMAX, and SpX-SVR (corresponding distributions for SpVAR-tt and SpVAR-cc models were omitted due to their high similarity to the SpX-ARIMAX model).  
Spatial distributions were calculated by the averaging of the obtained time-specific MAE values by detectors, while temporal distributions were calculated by averaging the detector-specific MAE values over time of the day.  
Figure 5: Density of mean absolute error (MAE) values: (**a**) spatially aggregated and (**b**) temporarily aggregated.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Calibrated**} & \multirow{2}{*}{**MAE by Forecasting Horizon**} & \multicolumn{3}{c}{**RMSE by Forecasting Horizon**} \\  & & \multicolumn{1}{c}{**Hypermeters’ Values**} & & & & & \\ \hline  & & 0–5 min & 5–10 min & 10–15 min & 0–5 min & 5–10 min & 10–15 min \\  & & (\(h=1\)) & (\(h=2\)) & (\(h=3\)) & (\(h=1\)) & (\(h=2\)) & (\(h=3\)) \\ \hline  & & \multicolumn{6}{c}{Transferred models} \\ \hline  & & & & & & & \\ SpX-lm & \(r_{1}=10\) & & & & & & \\  & \(r_{2}=30\) & 11.27 & 11.68 & 11.90 & 16.42 & 17.04 & 17.41 \\ SpX-SVR & \(r_{1}=10\) & & & & & & \\  & \(r_{2}=30\) & 10.54 & 10.83 & 11.08 & 15.78 & 16.17 & 16.51 \\  & \(r_{1}=10\) & & & & & & \\ SpX-ARIMAX & \(r_{2}=30\) & **8.85** & 9.56 & 9.91 & 12.54 & 13.75 & 14.33 \\  & \(w=w_{1/4}\) & & & & & & \\ GCNN & \(w=w_{1/4}\) & 9.77 & 10.57 & 11.16 & 18.62 & 23.37 & 25.95 \\ \hline  & & \multicolumn{6}{c}{Baseline models} \\ \hline SpVAR-tt & - & 8.92 & 9.42 & 9.84 & 12.58 & 13.40 & 14.09 \\ SpVAR-cc & \(\theta=0.1\) & 8.88 & **9.35** & **9.80** & **12.51** & **13.27** & **14.02** \\ VAR & \(p=6\) & 12.61 & 12.66 & 12.68 & 17.40 & 17.57 & 17.72 \\ ARIMA & detector-specific \(p\), \(q\) & 9.02 & 9.80 & 10.57 & 12.74 & 14.09 & 15.56 \\ Naive & - & 16.21 & 16.59 & 16.83 & 25.37 & 25.85 & 26.26 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Forecasting accuracy of the research models.