绘制多类问题的 ROC 曲线

Question

我正在尝试将sklearn ROC extension to multiclass 的想法应用于我的数据集。我的每类 ROC 曲线看起来都是一条直线，取消了 sklearn 的示例，显示曲线的波动。

我在下面给出一个 MWE 来说明我的意思：

# all imports
import numpy as np
import matplotlib.pyplot as plt
from itertools import cycle
from sklearn import svm, datasets
from sklearn.metrics import roc_curve, auc
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import label_binarize
from sklearn.datasets import  make_classification
from sklearn.ensemble import RandomForestClassifier
# dummy dataset
X, y = make_classification(10000, n_classes=5, n_informative=10, weights=[.04, .4, .12, .5, .04])
train, test, ytrain, ytest = train_test_split(X, y, test_size=.3, random_state=42)

# random forest model
model = RandomForestClassifier()
model.fit(train, ytrain)
yhat = model.predict(test)

然后以下函数绘制 ROC 曲线：

def plot_roc_curve(y_test, y_pred):
  
  n_classes = len(np.unique(y_test))
  y_test = label_binarize(y_test, classes=np.arange(n_classes))
  y_pred = label_binarize(y_pred, classes=np.arange(n_classes))

  # Compute ROC curve and ROC area for each class
  fpr = dict()
  tpr = dict()
  roc_auc = dict()
  for i in range(n_classes):
    fpr[i], tpr[i], _ = roc_curve(y_test[:, i], y_pred[:, i])
    roc_auc[i] = auc(fpr[i], tpr[i])
  
  # Compute micro-average ROC curve and ROC area
  fpr["micro"], tpr["micro"], _ = roc_curve(y_test.ravel(), y_pred.ravel())
  roc_auc["micro"] = auc(fpr["micro"], tpr["micro"])

  # First aggregate all false positive rates
  all_fpr = np.unique(np.concatenate([fpr[i] for i in range(n_classes)]))

  # Then interpolate all ROC curves at this points
  mean_tpr = np.zeros_like(all_fpr)
  for i in range(n_classes):
    mean_tpr += np.interp(all_fpr, fpr[i], tpr[i])

  # Finally average it and compute AUC
  mean_tpr /= n_classes

  fpr["macro"] = all_fpr
  tpr["macro"] = mean_tpr
  roc_auc["macro"] = auc(fpr["macro"], tpr["macro"])

  # Plot all ROC curves
  #plt.figure(figsize=(10,5))
  plt.figure(dpi=600)
  lw = 2
  plt.plot(fpr["micro"], tpr["micro"],
    label="micro-average ROC curve (area = {0:0.2f})".format(roc_auc["micro"]),
    color="deeppink", linestyle=":", linewidth=4,)

  plt.plot(fpr["macro"], tpr["macro"],
    label="macro-average ROC curve (area = {0:0.2f})".format(roc_auc["macro"]),
    color="navy", linestyle=":", linewidth=4,)

  colors = cycle(["aqua", "darkorange", "darkgreen", "yellow", "blue"])
  for i, color in zip(range(n_classes), colors):
    plt.plot(fpr[i], tpr[i], color=color, lw=lw,
        label="ROC curve of class {0} (area = {1:0.2f})".format(i, roc_auc[i]),)

  plt.plot([0, 1], [0, 1], "k--", lw=lw)
  plt.xlim([0.0, 1.0])
  plt.ylim([0.0, 1.05])
  plt.xlabel("False Positive Rate")
  plt.ylabel("True Positive Rate")
  plt.title("Receiver Operating Characteristic (ROC) curve")
  plt.legend()

输出：

plot_roc_curve(ytest, yhat)

一种直线弯曲一次。我想看看模型在不同阈值下的表现，而不仅仅是一个，类似于sklearn's illustration 3-classes 的图如下所示：

Answer 1

• 重点是您使用predict() 而不是predict_proba()/decision_function() 来定义您的y_hat。这意味着 - 考虑到阈值向量是由 y_hat 中的不同值的数量定义的（请参阅 here 以供参考），您将在每个类 only 上拥有很少的阈值 @987654329 @ 和 fpr 被计算（这反过来意味着你的曲线只在几个点被评估）。

• 确实，请考虑doc 所说的要传递给roc_curve() 中的y_scores 的内容，可能是概率估计值或决策值。在sklearn 的示例中，决策值用于计算分数。鉴于您正在考虑使用 RandomForestClassifier()，因此应该考虑在 y_hat 中进行概率估计。

• label-binarizing 输出的意义何在？ ROC 的标准定义是二进制分类。要传递给多类问题，您必须使用 OneVsAll 方法将问题转换为二进制，这样您将拥有n_class 数量的 ROC 曲线。 （实际上，请注意，SVC() 默认以 OvO 方式处理多类问题，在示例中，他们必须通过应用 OneVsRestClassifier 构造函数来强制使用 OvA；使用 RandomForestClassifier 你没有这样的问题这本质上是多类的，请参阅here 以供参考）。用这些术语来说，一旦你切换到predict_proba()，你会发现标签二值化预测没有多大意义。

   # all imports
   import numpy as np
   import matplotlib.pyplot as plt
   from itertools import cycle
   from sklearn import svm, datasets
   from sklearn.metrics import roc_curve, auc
   from sklearn.model_selection import train_test_split
   from sklearn.preprocessing import label_binarize
   from sklearn.datasets import  make_classification
   from sklearn.ensemble import RandomForestClassifier
   # dummy dataset
   X, y = make_classification(10000, n_classes=5, n_informative=10, weights=[.04, .4, .12, .5, .04])
   train, test, ytrain, ytest = train_test_split(X, y, test_size=.3, random_state=42)
  
   # random forest model
   model = RandomForestClassifier()
   model.fit(train, ytrain)
   yhat = model.predict_proba(test)
  
   def plot_roc_curve(y_test, y_pred):
       n_classes = len(np.unique(y_test))
       y_test = label_binarize(y_test, classes=np.arange(n_classes))
  
       # Compute ROC curve and ROC area for each class
       fpr = dict()
       tpr = dict()
       roc_auc = dict()
       thresholds = dict()
       for i in range(n_classes):
         fpr[i], tpr[i], thresholds[i] = roc_curve(y_test[:, i], y_pred[:, i], drop_intermediate=False)
       roc_auc[i] = auc(fpr[i], tpr[i])
  
       # Compute micro-average ROC curve and ROC area
       fpr["micro"], tpr["micro"], _ = roc_curve(y_test.ravel(), y_pred.ravel())
       roc_auc["micro"] = auc(fpr["micro"], tpr["micro"])
  
       # First aggregate all false positive rates
       all_fpr = np.unique(np.concatenate([fpr[i] for i in range(n_classes)]))
  
       # Then interpolate all ROC curves at this points
       mean_tpr = np.zeros_like(all_fpr)
       for i in range(n_classes):
         mean_tpr += np.interp(all_fpr, fpr[i], tpr[i])
  
       # Finally average it and compute AUC
       mean_tpr /= n_classes
  
       fpr["macro"] = all_fpr
       tpr["macro"] = mean_tpr
       roc_auc["macro"] = auc(fpr["macro"], tpr["macro"])
  
       # Plot all ROC curves
       #plt.figure(figsize=(10,5))
       plt.figure(dpi=600)
       lw = 2
       plt.plot(fpr["micro"], tpr["micro"],
       label="micro-average ROC curve (area = {0:0.2f})".format(roc_auc["micro"]),
       color="deeppink", linestyle=":", linewidth=4,)
  
       plt.plot(fpr["macro"], tpr["macro"],
       label="macro-average ROC curve (area = {0:0.2f})".format(roc_auc["macro"]),
       color="navy", linestyle=":", linewidth=4,)
  
       colors = cycle(["aqua", "darkorange", "darkgreen", "yellow", "blue"])
       for i, color in zip(range(n_classes), colors):
         plt.plot(fpr[i], tpr[i], color=color, lw=lw,
         label="ROC curve of class {0} (area = {1:0.2f})".format(i, roc_auc[i]),)
  
       plt.plot([0, 1], [0, 1], "k--", lw=lw)
       plt.xlim([0.0, 1.0])
       plt.ylim([0.0, 1.05])
       plt.xlabel("False Positive Rate")
       plt.ylabel("True Positive Rate")
       plt.title("Receiver Operating Characteristic (ROC) curve")
       plt.legend()
  

最后，考虑到roc_curve() 也有一个drop_intermediate 参数，用于删除次优阈值（了解它可能很有用）。