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.