Loss functions Part I

Designing Machine Learning Workflows in Python

Dr. Chris Anagnostopoulos

Honorary Associate Professor

The KDD '99 cup dataset

kdd.iloc[0]

kdd.iloc[0]
duration                         51
protocol_type                   tcp
service                        smtp
flag                             SF
src_bytes                      1169
dst_bytes                       332
land                              0
...
dst_host_rerror_rate              0
dst_host_srv_rerror_rate          0
label                          good

False positives vs false negatives

Binarize label:

kdd['label'] = kdd['label'] == 'bad'

Fit a Gaussian Naive Bayes classifier:

clf = GaussianNB().fit(X_train, y_train)
predictions = clf.predict(X_test)
results = pd.DataFrame({
    'actual': y_test,
    'predicted': predictions
})

False positives vs false negatives

Binarize label:

kdd['label'] = kdd['label'] == 'bad'

Fit a Gaussian Naive Bayes classifier:

clf = GaussianNB().fit(X_train, y_train)
predictions = clf.predict(X_test)
results = pd.DataFrame({
    'actual': y_test,
    'predicted': predictions
})

There are four possible configurations of labels versus predictions: both True, both False, a label of True with a prediction of False, and a label of False with a prediction of True. The latter combination is highlighted here.

False positives vs false negatives

Binarize label:

kdd['label'] = kdd['label'] == 'bad'

Fit a Gaussian Naive Bayes classifier:

clf = GaussianNB().fit(X_train, y_train)
predictions = clf.predict(X_test)
results = pd.DataFrame({
    'actual': y_test,
    'predicted': predictions
})

Now, the combination of the label True and the prediction False is highlighted instead.

False positives vs false negatives

Binarize label:

kdd['label'] = kdd['label'] == 'bad'

Fit a Gaussian Naive Bayes classifier:

clf = GaussianNB().fit(X_train, y_train)
predictions = clf.predict(X_test)
results = pd.DataFrame({
    'actual': y_test,
    'predicted': predictions
})

The two cases where the prediction agrees with the labels are highlighted now.

The confusion matrix

conf_mat = confusion_matrix(
    ground_truth, predictions)

array([[9477,   19],
       [ 397, 2458]])

tn, fp, fn, tp = conf_mat.ravel()
(fp, fn)

(19, 397)

A confusion matrix, counting the cases for each of the four combinations mentioned before for this particular dataset.

Scalar performance metrics

accuracy = 1-(fp + fn)/len(ground_truth)

recall = tp/(tp+fn)

fpr = fp/(tn+fp)

precision = tp/(tp+fp)

f1 = 2*(precision*recall)/(precision+recall)

accuracy_score(ground_truth, predictions)
recall_score(ground_truth, predictions)
precision_score(ground_truth, predictions)
f1_score(ground_truth, predictions)

False positives vs false negatives

Classifier A:

tn, fp, fn, tp = confusion_matrix(
    ground_truth, predictions_A).ravel()
(fp,fn)

(3, 3)

cost = 10 * fp + fn

Classifier B:

tn, fp, fn, tp = confusion_matrix(
    ground_truth, predictions_B).ravel()
(fp,fn)

(0, 26)

cost = 10 * fp + fn

Which classifier is better?

Designing Machine Learning Workflows in Python