求ROC的算法

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求ROC的算法！

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关键词：ROC

同求，坐等帮助。

在SPSS17.0的医学应用统计学中有讲到

http://alexkong.net/2013/06/introduction-to-auc-and-roc/
这篇博文讲的很清楚，什么是ROC，怎么绘图，已经AUC的计算

先算sensitivity, specificity

stackexchange上面很好的回答：
https://stats.stackexchange.com/a/132832/133228

Abbreviations

AUC = Area Under the Curve.
AUROC = Area Under the Receiver Operating Characteristic curve.
AUC is used most of the time to mean AUROC, which is a bad practice since as Marc Claesen pointed out AUC is ambiguous (could be any curve) while AUROC is not.

Interpreting the AUROC

The AUROC has several equivalent interpretations:

The expectation that a uniformly drawn random positive is ranked before a uniformly drawn random negative.
The expected proportion of positives ranked before a uniformly drawn random negative.
The expected true positive rate if the ranking is split just before a uniformly drawn random negative.
The expected proportion of negatives ranked after a uniformly drawn random positive.
The expected false positive rate if the ranking is split just after a uniformly drawn random positive.
Computing the AUROC

Assume we have a probabilistic, binary classifier such as logistic regression.

Before presenting the ROC curve (= Receiver Operating Characteristic curve), the concept of confusion matrix must be understood. When we make a binary prediction, there can be 4 types of outcomes:

We predict 0 while we should have the class is actually 0: this is called a True Negative, i.e. we correctly predict that the class is negative (0). For example, an antivirus did not detect a harmless file as a virus .
We predict 0 while we should have the class is actually 1: this is called a False Negative, i.e. we incorrectly predict that the class is negative (0). For example, an antivirus failed to detect a virus.
We predict 1 while we should have the class is actually 0: this is called a False Positive, i.e. we incorrectly predict that the class is positive (1). For example, an antivirus considered a harmless file to be a virus.
We predict 1 while we should have the class is actually 1: this is called a True Positive, i.e. we correctly predict that the class is positive (1). For example, an antivirus rightfully detected a virus.
To get the confusion matrix, we go over all the predictions made by the model, and count how many times each of those 4 types of outcomes occur:

enter image description here

In this example of a confusion matrix, among the 50 data points that are classified, 45 are correctly classified and the 5 are misclassified.

Since to compare two different models it is often more convenient to have a single metric rather than several ones, we compute two metrics from the confusion matrix, which we will later combine into one:

True positive rate (TPR), aka. sensitivity, hit rate, and recall

. Intuitively this metric corresponds to the proportion of positive data points that are correctly considered as positive, with respect to all positive data points. In other words, the higher TPR, the fewer positive data points we will miss.
False positive rate (FPR), aka. fall-out,

. Intuitively this metric corresponds to the proportion of negative data points that are mistakenly considered as positive, with respect to all negative data points. In other words, the higher FPR, the more negative data points we will missclassified.
To combine the FPR and the TPR into one single metric, we first compute the two former metrics with many different threshold