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# Metric Functions

Compute metrics for assessing the performance of classification/regression models.

The Confusion Matrix:

Total Samples (ts) | Actual Positives (ap) | Actual Negatives (an)
Predicted Positives (pp) | True Positives (tp) | False Positives (fp)
Predicted Negatives (pn) | False Negatives (fn) | True Negatives (tn)

`mlpy.``err`(y, p)

  Compute the Error.

  error = (fp + fn) / ts

  Input

  > - y - classes (two classes) [1D numpy array integer]
  > - p - prediction (two classes) [1D numpy array integer]

  Output

  > - error

`mlpy.``errp`(y, p)

  Compute the Error for positive samples.

  errp = fp / ap

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - p - prediction (two classes +1 and -1) [1D numpy array integer]

  Output

  > - error for positive samples

`mlpy.``errn`(y, p)

  Compute the Error for negative samples.

  errn = fn / an

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - p - prediction (two classes +1 and -1) [1D numpy array integer]

  Output

  > - error for negative samples

`mlpy.``acc`(y, p)

  Compute the Accuracy.

  accuracy = (tp + tn) / ts

  Input

  > - y - classes (two classes) [1D numpy array integer]
  > - p - prediction (two classes) [1D numpy array integer]

  Output

  > - accuracy

`mlpy.``sens`(y, p)

  Compute the Sensitivity.

  sensitivity = tp / ap

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - p - prediction (two classes +1 and -1) [1D numpy array integer]

  Output

  > - sensitivity

`mlpy.``spec`(y, p)

  Compute the Specificity.

  specificity = tn / an

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - p - prediction (two classes +1 and -1) [1D numpy array integer]

  Output

  > - specificity

`mlpy.``single_auc`(y, p)

  Compute the single AUC.

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - p - prediction (two classes +1 and -1) [1D numpy array integer]

  Output

  > - singleAUC

`mlpy.``wmw_auc`(y, r)

  Compute the AUC by using the Wilcoxon-Mann-Whitney formula.

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - r - real-valued prediction [1D numpy array float]

  Output

  > - wmwAUC

`mlpy.``ppv`(y, p)

  Compute the Positive Predictive Value (PPV).

  PPV = tp / pp

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - p - prediction (two classes +1 and -1) [1D numpy array integer]

  Output

  > - PPV

`mlpy.``npv`(y, p)

  Compute the Negative Predictive Value (NPV).

  NPV = tn / pn

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - p - prediction (two classes +1 and -1) [1D numpy array integer]

  Output

  > - NPV

`mlpy.``mcc`(y, p)

  Compute the Matthews Correlation Coefficient (MCC).

  MCC = ((tp*tn)-(fp*fn)) / sqrt((tp+fn)*(tp+fp)*(tn+fn)*(tn+fp))

  Input

  > - y - classes (two classes +1 and -1) [1D numpy array integer]
  > - p - prediction (two classes +1 and -1) [1D numpy array integer]

  Output

  > - MCC

`mlpy.``mse`(y, p)

  Mean Squared Error

`mlpy.``r2`(y, p)

  Coefficient of determination (R^2)

  R^2 is computed as square of the correlation coefficient.

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