How to interpret almost perfect accuracy and AUC-ROC but zero f1-score, precision and recall

Question

I am training ML logistic classifier to classify two classes using python scikit-learn. They are in an extremely imbalanced data (about 14300:1). I'm getting almost 100% accuracy and ROC-AUC, but 0% in precision, recall, and f1 score. I understand that accuracy is usually not useful in very imbalanced data, but why is the ROC-AUC measure is close to perfect as well?

from sklearn.metrics import roc_curve, auc

# Get ROC 
y_score = classifierUsed2.decision_function(X_test)
false_positive_rate, true_positive_rate, thresholds = roc_curve(y_test, y_score)
roc_auc = auc(false_positive_rate, true_positive_rate)
print 'AUC-'+'=',roc_auc

1= class1
0= class2
Class count:
0    199979
1        21

Accuracy: 0.99992
Classification report:
             precision    recall  f1-score   support

          0       1.00      1.00      1.00     99993
          1       0.00      0.00      0.00         7

avg / total       1.00      1.00      1.00    100000

Confusion matrix:
[[99992     1]
 [    7     0]]
AUC= 0.977116255281

The above is using logistic regression, below is using decision tree, the decision matrix looks almost identical, but the AUC is a lot different.

1= class1
0= class2
Class count:
0    199979
1        21
Accuracy: 0.99987
Classification report:
             precision    recall  f1-score   support

          0       1.00      1.00      1.00     99989
          1       0.00      0.00      0.00        11

avg / total       1.00      1.00      1.00    100000

Confusion matrix:
[[99987     2]
 [   11     0]]
AUC= 0.4999899989

you may want to give us the confusion matrix. Intuitively, I would guess that this is not possible, but I don't have the time to do the math right now. — cel
Thanks for the suggestions, I have added the codes and results — KubiK888
Interpretation: You do not have any predictability. You have basically no examples for class 1 and predict all wrong. You are better off simply predicting 0 all the time. — cel
Yes I understand, but does this affect both accuracy and AUC-ROC measures? Or is my AUC-ROC calculation wrong? — KubiK888
Yes, your model has high accuracy and high AUC, is that what you ask? But that's because almost all data in your test set are 0 and you basically predict only zeros. No, this does not show that your model is useful. I tried to give you an intuition for that. Compare the AUC and accuracy for a model that always predicts 0. Obviously this is not a useful model. But it will score better. This is due to the structure of the test set. Get a balanced test set and things will be much clearer. — cel

lejlot lejlot · Accepted Answer · 2016-01-09T21:05:23

One must understand crucial difference between AUC ROC and "point-wise" metrics like accuracy/precision etc. ROC is a function of a threshold. Given a model (classifier) that outputs the probability of belonging to each class, we predict the class that has the highest probability (support). However, sometimes we can get better scores by changing this rule and requiring one support to be 2 times bigger than the other to actually classify as a given class. This is often true for imbalanced datasets. This way you are actually modifying the learned prior of classes to better fit your data. ROC looks at "what would happen if I change this threshold to all possible values" and then AUC ROC computes the integral of such a curve.

Consequently:

high AUC ROC vs low f1 or other "point" metric, means that your classifier currently does a bad job, however you can find the threshold for which its score is actually pretty decent
low AUC ROC and low f1 or other "point" metric, means that your classifier currently does a bad job, and even fitting a threshold will not change it
high AUC ROC and high f1 or other "point" metric, means that your classifier currently does a decent job, and for many other values of threshold it would do the same
low AUC ROC vs high f1 or other "point" metric, means that your classifier currently does a decent job, however for many other values of threshold - it is pretty bad

How to interpret almost perfect accuracy and AUC-ROC but zero f1-score, precision and recall

1 Answers