Why KS curve starts with (0,0)? - machine-learning

Question

the vertical axis of the KS curve is tpr,fpr and (tpr-fpr), the horizontal axis is the threshold.
tpr=(tp/tp+fn).
When the threshold = 0 , predict all the sample to 1,so the tp = number of positive samples , fn = 0.
Thus, the tpr=1.
But all the KS curves I found on the Internet begin with (0,0). Shouldn't it be (0,1)? I am so confused! Thanks for answering！

Answer 1

TP: number of positive prediction which actually are 1
FP: number of positive predition which actually are 0
TN: number of negative prediction which actually are 0
FN: number of negative predition which actually are 1
When threthoud = 0, model only predicts positive, so that FN=TN=0. FPR = FP/(FP+TN) = 1, TPR=TP/(TP+FN) = 1, so this point should be (1,1). You make a mistake that
When threthoud = 1 , model only predicts negative, so that TP = FP = 0. FPR = FP/(FP+TN) = 0, TPR=TP/(TP+FN) = 0, so this point should be (0,0).
# roc curve and auc
from sklearn.datasets import make_classification
from sklearn.neighbors import KNeighborsClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import roc_curve
from sklearn.metrics import roc_auc_score
from matplotlib import pyplot
import pandas as pd
# generate 2 class dataset
X, y = make_classification(n_samples=1000, n_classes=2, weights=[1,1], random_state=1)
# split into train/test sets
trainX, testX, trainy, testy = train_test_split(X, y, test_size=0.5, random_state=2)
# fit a model
model = KNeighborsClassifier(n_neighbors=3)
model.fit(trainX, trainy)
# predict probabilities
probs = model.predict_proba(testX)
# keep probabilities for the positive outcome only
probs = probs[:, 1]
# calculate AUC
auc = roc_auc_score(testy, probs)
print('AUC: %.3f' % auc)
# calculate roc curve
fpr, tpr, thresholds = roc_curve(testy, probs)
# plot no skill
pyplot.plot([0, 1], [0, 1], linestyle='--')
# plot the roc curve for the model
pyplot.plot(fpr, tpr, marker='.')
# show the plot
pyplot.show()
# see calculations
pd.DataFrame({'fpr':fpr,'tpr':tpr,'thresholds':thresholds})
Outputs:
fpr tpr threshouds
0 0.000000 0.000000 2.000000
1 0.054264 0.561983 1.000000
2 0.217054 0.884298 0.666667
3 0.406977 0.975207 0.333333
4 1.000000 1.000000 0.000000