Regression Metrics
STT |
Metric |
Metric Fullname |
Characteristics |
---|---|---|---|
1 |
EVS |
Explained Variance Score |
Bigger is better (Best = 1), Range=(-inf, 1.0] |
2 |
ME |
Max Error |
Smaller is better (Best = 0), Range=[0, +inf) |
3 |
MBE |
Mean Bias Error |
Best = 0, Range=(-inf, +inf) |
4 |
MAE |
Mean Absolute Error |
Smaller is better (Best = 0), Range=[0, +inf) |
5 |
MSE |
Mean Squared Error |
Smaller is better (Best = 0), Range=[0, +inf) |
6 |
RMSE |
Root Mean Squared Error |
Smaller is better (Best = 0), Range=[0, +inf) |
7 |
MSLE |
Mean Squared Log Error |
Smaller is better (Best = 0), Range=[0, +inf) |
8 |
MedAE |
Median Absolute Error |
Smaller is better (Best = 0), Range=[0, +inf) |
9 |
MRE / MRB |
Mean Relative Error / Mean Relative Bias |
Smaller is better (Best = 0), Range=[0, +inf) |
10 |
MPE |
Mean Percentage Error |
Best = 0, Range=(-inf, +inf) |
11 |
MAPE |
Mean Absolute Percentage Error |
Smaller is better (Best = 0), Range=[0, +inf) |
12 |
SMAPE |
Symmetric Mean Absolute Percentage Error |
Smaller is better (Best = 0), Range=[0, 1] |
13 |
MAAPE |
Mean Arctangent Absolute Percentage Error |
Smaller is better (Best = 0), Range=[0, +inf) |
14 |
MASE |
Mean Absolute Scaled Error |
Smaller is better (Best = 0), Range=[0, +inf) |
15 |
NSE |
Nash-Sutcliffe Efficiency Coefficient |
Bigger is better (Best = 1), Range=(-inf, 1] |
16 |
NNSE |
Normalized Nash-Sutcliffe Efficiency Coefficient |
Bigger is better (Best = 1), Range=[0, 1] |
17 |
WI |
Willmott Index |
Bigger is better (Best = 1), Range=[0, 1] |
18 |
R / PCC |
Pearson’s Correlation Coefficient |
Bigger is better (Best = 1), Range=[-1, 1] |
19 |
AR / APCC |
Absolute Pearson’s Correlation Coefficient |
Bigger is better (Best = 1), Range=[-1, 1] |
20 |
RSQ/R2S |
(Pearson’s Correlation Index) ^ 2 |
Bigger is better (Best = 1), Range=[0, 1] |
21 |
R2 / COD |
Coefficient of Determination |
Bigger is better (Best = 1), Range=(-inf, 1] |
22 |
AR2 / ACOD |
Adjusted Coefficient of Determination |
Bigger is better (Best = 1), Range=(-inf, 1] |
23 |
CI |
Confidence Index |
Bigger is better (Best = 1), Range=(-inf, 1] |
24 |
DRV |
Deviation of Runoff Volume |
Smaller is better (Best = 1.0), Range=[1, +inf) |
25 |
KGE |
Kling-Gupta Efficiency |
Bigger is better (Best = 1), Range=(-inf, 1] |
26 |
GINI |
Gini Coefficient |
Smaller is better (Best = 0), Range=[0, +inf) |
27 |
GINI_WIKI |
Gini Coefficient on Wikipage |
Smaller is better (Best = 0), Range=[0, +inf) |
28 |
PCD |
Prediction of Change in Direction |
Bigger is better (Best = 1.0), Range=[0, 1] |
29 |
CE |
Cross Entropy |
Range(-inf, 0], Can’t give comment about this |
30 |
KLD |
Kullback Leibler Divergence |
Best = 0, Range=(-inf, +inf) |
31 |
JSD |
Jensen Shannon Divergence |
Smaller is better (Best = 0), Range=[0, +inf) |
32 |
VAF |
Variance Accounted For |
Bigger is better (Best = 100%), Range=(-inf, 100%] |
33 |
RAE |
Relative Absolute Error |
Smaller is better (Best = 0), Range=[0, +inf) |
34 |
A10 |
A10 Index |
Bigger is better (Best = 1), Range=[0, 1] |
35 |
A20 |
A20 Index |
Bigger is better (Best = 1), Range=[0, 1] |
36 |
A30 |
A30 Index |
Bigger is better (Best = 1), Range=[0, 1] |
37 |
NRMSE |
Normalized Root Mean Square Error |
Smaller is better (Best = 0), Range=[0, +inf) |
38 |
RSE |
Residual Standard Error |
Smaller is better (Best = 0), Range=[0, +inf) |
39 |
RE / RB |
Relative Error / Relative Bias |
Best = 0, Range=(-inf, +inf) |
40 |
AE |
Absolute Error |
Best = 0, Range=(-inf, +inf) |
41 |
SE |
Squared Error |
Smaller is better (Best = 0), Range=[0, +inf) |
42 |
SLE |
Squared Log Error |
Smaller is better (Best = 0), Range=[0, +inf) |
43 |
COV |
Covariance |
Bigger is better (No best value), Range=(-inf, +inf) |
44 |
COR |
Correlation |
Bigger is better (Best = 1), Range=[-1, +1] |
45 |
EC |
Efficiency Coefficient |
Bigger is better (Best = 1), Range=(-inf, +1] |
46 |
OI |
Overall Index |
Bigger is better (Best = 1), Range=(-inf, +1] |
47 |
CRM |
Coefficient of Residual Mass |
Smaller is better (Best = 0), Range=(-inf, +inf) |
From now on:
\(\hat{y}\) is the estimated target output,
\(y\) is the corresponding (correct) target output.
\(\hat{Y}\) is the whole estimated target output ,
\(Y\) is the corresponding (correct) target output.
\(mean(\hat{Y})\) is the mean of whole estimated target output ,
\(mean(Y)\) is the mean of whole (correct) target output.
- EVS - Explained Variance Score
- ME - Max Error
- MAE - Mean Absolute Error
- MSE - Mean Squared Error
- BE - Mean Bias Error
- RMSE - Root Mean Square Error
- MSLE - Mean Squared Logarithmic Error
- MedAE - Median Absolute Error
- MRE - Mean Relative Error
- MPE - Mean Percentage Error
- MAPE - Mean Absolute Percentage Error
- SMAPE - Symmetric Mean Absolute Percentage Error
- MAAPE - Mean Arctangent Absolute Percentage Error
- MASE - Mean Absolute Scaled Error
- NSE - Nash-Sutcliffe Efficiency
- NNSE - Normalized NSE
- WI - Willmott Index
- R - Pearson’s Correlation Index
- AR - Absolute Pearson’s Correlation Index
- R2 - Coefficient of Determination
- AR2 - Adjusted R2
- CI - Confidence Index
- R2s - (Pearson’s Correlation Index)**2
- DRV - Deviation of Runoff Volume
- KGE - Kling-Gupta Efficiency
- GINI - GINI Coefficient
- PCD - Prediction of Change in Direction
- CE - Cross Entropy
- KLD - Kullback-Leibler Divergence
- JSD - Jensen-Shannon Divergence
- VAF - Variance Accounted For
- RAE - Relative Absolute Error
- A10 - A10 index
- A20 - A20 index
- A30 - A30 index
- NRMSE - Normalized Root Mean Square Error
- RSE - Residual Standard Error
- COV - Covariance
- COR - Correlation
- EC - Efficiency Coefficient
- OI - Overall Index
- CRM - Coefficient of Residual Mass
- RE - Relative Error
- AE - Absolute Error
- SE - Squared Error
- SLE - Squared Log Error