Advances, Systems and Applications
Table 2 Selected regression evaluation metrics, their formulas, and symbols
From: VTGAN: hybrid generative adversarial networks for cloud workload prediction
Performance Metric | Equation |
|---|---|
Root Mean Squared Error (RMSE) | \(\text {RMSE}=\sqrt{\frac{1}{T} \sum _{t=1}^{T} ( i_{t}-\hat{i}_{t})^2}\) |
Mean Absolute Percentage Error | \(\text {MAPE}=\frac{1}{T}\sum _{t=1}^{T} \frac{\mid i_{t}- \hat{i}_{t}\mid }{i_{t}}\times 100\%\) |
(MAPE) | Â |
Mean Absolute Error (MAE) | \(\text {MAE}=\frac{1}{T}\sum _{t=1}^{T} \mid i_{t}-\hat{i}_{t} \mid\) |
Theil’s coefficient (Theil) [80] | \(\text {Theil}= \frac{\sqrt{\frac{1}{T} \sum _{t=1}^{T} ( i_{t}- \hat{i}_{t})^2}}{\sqrt{\frac{1}{T} \sum _{t=1}^{T} ( i_{t})^2} +\sqrt{\frac{1}{T} \sum _{t=1}^{T} ( \hat{i}_{t})^2} }\) |
Average relative variance (ARV) [11] | \(\text {ARV}= \frac{\sum _{t=1}^{T} (i_{t}- \hat{i}_{t})^2}{\sum _{t=1}^{T} (\hat{i}_{t}- i)}\) |
[11] | Â |
Prediction of Change in Direction | \(\text {POCID}= \frac{\sum _{t=1}^{T} D_t}{T} \times 100\) |
(POCID) [11] | where \(D_t= \left\{ \begin{array}{ll} 1, &{} \text {if}\ (i_{t}-i_{t-1})(\hat{i}_{t}- \hat{i}_{t-1}) > 0,\\ 0, &{} otherwise. \end{array}\right.\) |
Coefficient of determination (\(R^2\)) [11] | \(R^2= 1- \frac{\sum _{t=1}^{T} ( i_{t}- \hat{i}_{t})^2}{\sum _{t=1}^{T} ( i_{t}- \bar{i})^2}\) |