How to Plot PR-Curve Over 10 folds of Cross Validation in Scikit-Learn

Question

I'm running some supervised experiments for a binary prediction problem. I'm using 10-fold cross validation to evaluate performance in terms of mean average precision (average precision for each fold divided by the number of folds for cross validation - 10 in my case). I would like to plot PR-curves of the result of mean average precision over these 10 folds, however I'm not sure the best way to do this.

A previous question in the Cross Validated Stack Exchange site raised this same problem. A comment recommended working through this example on plotting ROC curves across folds of cross validation from the Scikit-Learn site, and tailoring it to average precision. Here is the relevant section of code I've modified to try this idea:

from scipy import interp
# Other packages/functions are imported, but not crucial to the question
max_ent = LogisticRegression()

mean_precision = 0.0
mean_recall = np.linspace(0,1,100)
mean_average_precision = []

for i in set(folds):
    y_scores = max_ent.fit(X_train, y_train).decision_function(X_test)
    precision, recall, _ = precision_recall_curve(y_test, y_scores)
    average_precision = average_precision_score(y_test, y_scores)
    mean_average_precision.append(average_precision)
    mean_precision += interp(mean_recall, recall, precision)

# After this line of code, inspecting the mean_precision array shows that 
# the majority of the elements equal 1. This is the part that is confusing me
# and is contributing to the incorrect plot.
mean_precision /= len(set(folds))
# This is what the actual MAP score should be
mean_average_precision = sum(mean_average_precision) / len(mean_average_precision)

# Code for plotting the mean average precision curve across folds
plt.plot(mean_recall, mean_precision)
plt.title('Mean AP Over 10 folds (area=%0.2f)' % (mean_average_precision))
plt.show()

The code runs, however in my case the mean average precision curve is incorrect. For some reason, the array I have assigned to store the mean_precision scores (mean_tpr variable in the ROC example) computes the first element to be near zero, and all other elements to be 1 after dividing by the number of folds. Below is a visualization of the mean_precision scores plotted against the mean_recall scores. As you can see, the plot jumps to 1 which is inaccurate. So my hunch is something is going awry in the update of mean_precision (mean_precision += interp(mean_recall, recall, precision) ) at in each fold of cross-validation, but it's unclear how to fix this. Any guidance or help would be appreciated.

Answer 1

Adding to @Dietmar's answer, I agree that it's mostly correct, except instead of using sklearn.metrics.auc to compute area under precision recall curve, I think we should be using sklearn.metrics.average_precision_score.

Supporting literature:

1. Davis, J., & Goadrich, M. (2006, June). The relationship between Precision-Recall and ROC curves. In Proceedings of the 23rd international conference on Machine learning (pp. 233-240).

For example, in PR space it is incorrect to linearly interpolate between points

2. Boyd, K., Eng, K. H., & Page, C. D. (2013, September). Area under the precision-recall curve: point estimates and confidence intervals. In Joint European conference on machine learning and knowledge discovery in databases (pp. 451-466). Springer, Berlin, Heidelberg.

We provide evidence in favor of computing AUCPR using the lower trapezoid, average precision, or interpolated median estimators

From sklearn's documentation on average_precision_score

This implementation is not interpolated and is different from computing the area under the precision-recall curve with the trapezoidal rule, which uses linear interpolation and can be too optimistic.

Here's a fully reproducible example which I hope can help others if they cross this thread:

import matplotlib.pyplot as plt
import numpy as np
from numpy import interp
import pandas as pd
from sklearn.datasets import make_blobs
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score, auc, average_precision_score, confusion_matrix, roc_curve, precision_recall_curve
from sklearn.model_selection import KFold, train_test_split, RandomizedSearchCV, StratifiedKFold
from sklearn.svm import SVC

%matplotlib inline

def draw_cv_roc_curve(classifier, cv, X, y, title='ROC Curve'):
    """
    Draw a Cross Validated ROC Curve.
    Args:
        classifier: Classifier Object
        cv: StratifiedKFold Object: (https://stats.stackexchange.com/questions/49540/understanding-stratified-cross-validation)
        X: Feature Pandas DataFrame
        y: Response Pandas Series
    Example largely taken from http://scikit-learn.org/stable/auto_examples/model_selection/plot_roc_crossval.html#sphx-glr-auto-examples-model-selection-plot-roc-crossval-py
    """
    # Creating ROC Curve with Cross Validation
    tprs = []
    aucs = []
    mean_fpr = np.linspace(0, 1, 100)

    i = 0
    for train, test in cv.split(X, y):
        probas_ = classifier.fit(X.iloc[train], y.iloc[train]).predict_proba(X.iloc[test])
        # Compute ROC curve and area the curve
        fpr, tpr, thresholds = roc_curve(y.iloc[test], probas_[:, 1])
        tprs.append(interp(mean_fpr, fpr, tpr))
        
        tprs[-1][0] = 0.0
        roc_auc = auc(fpr, tpr)
        aucs.append(roc_auc)
        plt.plot(fpr, tpr, lw=1, alpha=0.3,
                 label='ROC fold %d (AUC = %0.2f)' % (i, roc_auc))

        i += 1
    plt.plot([0, 1], [0, 1], linestyle='--', lw=2, color='r',
             label='Luck', alpha=.8)
    
    mean_tpr = np.mean(tprs, axis=0)
    mean_tpr[-1] = 1.0
    mean_auc = auc(mean_fpr, mean_tpr)
    std_auc = np.std(aucs)
    plt.plot(mean_fpr, mean_tpr, color='b',
             label=r'Mean ROC (AUC = %0.2f $\pm$ %0.2f)' % (mean_auc, std_auc),
             lw=2, alpha=.8)

    std_tpr = np.std(tprs, axis=0)
    tprs_upper = np.minimum(mean_tpr + std_tpr, 1)
    tprs_lower = np.maximum(mean_tpr - std_tpr, 0)
    plt.fill_between(mean_fpr, tprs_lower, tprs_upper, color='grey', alpha=.2,
                     label=r'$\pm$ 1 std. dev.')

    plt.xlim([-0.05, 1.05])
    plt.ylim([-0.05, 1.05])
    plt.xlabel('False Positive Rate')
    plt.ylabel('True Positive Rate')
    plt.title(title)
    plt.legend(loc="lower right")
    plt.show()


def draw_cv_pr_curve(classifier, cv, X, y, title='PR Curve'):
    """
    Draw a Cross Validated PR Curve.
    Keyword Args:
        classifier: Classifier Object
        cv: StratifiedKFold Object: (https://stats.stackexchange.com/questions/49540/understanding-stratified-cross-validation)
        X: Feature Pandas DataFrame
        y: Response Pandas Series
        
    Largely taken from: https://stackoverflow.com/questions/29656550/how-to-plot-pr-curve-over-10-folds-of-cross-validation-in-scikit-learn
    """
    y_real = []
    y_proba = []

    i = 0
    for train, test in cv.split(X, y):
        probas_ = classifier.fit(X.iloc[train], y.iloc[train]).predict_proba(X.iloc[test])
        # Compute ROC curve and area the curve
        precision, recall, _ = precision_recall_curve(y.iloc[test], probas_[:, 1])
        
        # Plotting each individual PR Curve
        plt.plot(recall, precision, lw=1, alpha=0.3,
                 label='PR fold %d (AUC = %0.2f)' % (i, average_precision_score(y.iloc[test], probas_[:, 1])))
        
        y_real.append(y.iloc[test])
        y_proba.append(probas_[:, 1])

        i += 1
    
    y_real = np.concatenate(y_real)
    y_proba = np.concatenate(y_proba)
    
    precision, recall, _ = precision_recall_curve(y_real, y_proba)

    plt.plot(recall, precision, color='b',
             label=r'Precision-Recall (AUC = %0.2f)' % (average_precision_score(y_real, y_proba)),
             lw=2, alpha=.8)

    plt.xlim([-0.05, 1.05])
    plt.ylim([-0.05, 1.05])
    plt.xlabel('Recall')
    plt.ylabel('Precision')
    plt.title(title)
    plt.legend(loc="lower right")
    plt.show()

# Create a fake example where X is an 1000 x 2 Matrix
# Y is 1000 x 1 vector
# Binary Classification Problem
FOLDS = 5

X, y = make_blobs(n_samples=1000, n_features=2, centers=2, cluster_std=10.0,
    random_state=12345)

X = pd.DataFrame(X)
y = pd.DataFrame(y)

f, axes = plt.subplots(1, 2, figsize=(10, 5))

X.loc[y.iloc[:, 0] == 1]

axes[0].scatter(X.loc[y.iloc[:, 0] == 0, 0], X.loc[y.iloc[:, 0] == 0, 1], color='blue', s=2, label='y=0')
axes[0].scatter(X.loc[y.iloc[:, 0] !=0, 0], X.loc[y.iloc[:, 0] != 0, 1], color='red', s=2, label='y=1')
axes[0].set_xlabel('X[:,0]')
axes[0].set_ylabel('X[:,1]')
axes[0].legend(loc='lower left', fontsize='small')

# Setting up simple RF Classifier
clf = RandomForestClassifier()

# Set up Stratified K Fold
cv = StratifiedKFold(n_splits=6)

draw_cv_roc_curve(clf, cv, X, y, title='Cross Validated ROC')

draw_cv_pr_curve(clf, cv, X, y, title='Cross Validated PR Curve')

Answer 2

I had the same problem. Here is my solution: instead of averaging across the folds, I compute the precision_recall_curve across the results from all folds, after the loop. According to the discussion in https://stats.stackexchange.com/questions/34611/meanscores-vs-scoreconcatenation-in-cross-validation this is a generally preferable approach.

import matplotlib.pyplot as plt
import numpy
from sklearn.datasets import make_blobs
from sklearn.metrics import precision_recall_curve, auc
from sklearn.model_selection import KFold
from sklearn.svm import SVC

FOLDS = 5

X, y = make_blobs(n_samples=1000, n_features=2, centers=2, cluster_std=10.0,
    random_state=12345)

f, axes = plt.subplots(1, 2, figsize=(10, 5))

axes[0].scatter(X[y==0,0], X[y==0,1], color='blue', s=2, label='y=0')
axes[0].scatter(X[y!=0,0], X[y!=0,1], color='red', s=2, label='y=1')
axes[0].set_xlabel('X[:,0]')
axes[0].set_ylabel('X[:,1]')
axes[0].legend(loc='lower left', fontsize='small')

k_fold = KFold(n_splits=FOLDS, shuffle=True, random_state=12345)
predictor = SVC(kernel='linear', C=1.0, probability=True, random_state=12345)

y_real = []
y_proba = []
for i, (train_index, test_index) in enumerate(k_fold.split(X)):
    Xtrain, Xtest = X[train_index], X[test_index]
    ytrain, ytest = y[train_index], y[test_index]
    predictor.fit(Xtrain, ytrain)
    pred_proba = predictor.predict_proba(Xtest)
    precision, recall, _ = precision_recall_curve(ytest, pred_proba[:,1])
    lab = 'Fold %d AUC=%.4f' % (i+1, auc(recall, precision))
    axes[1].step(recall, precision, label=lab)
    y_real.append(ytest)
    y_proba.append(pred_proba[:,1])

y_real = numpy.concatenate(y_real)
y_proba = numpy.concatenate(y_proba)
precision, recall, _ = precision_recall_curve(y_real, y_proba)
lab = 'Overall AUC=%.4f' % (auc(recall, precision))
axes[1].step(recall, precision, label=lab, lw=2, color='black')
axes[1].set_xlabel('Recall')
axes[1].set_ylabel('Precision')
axes[1].legend(loc='lower left', fontsize='small')

f.tight_layout()
f.savefig('result.png')

Answer 3

I couldn't find an answer posted in other discussions, so hopefully this can help. The main thing was to reverse recall and precision before using interp:

reversed_recall = np.fliplr([recall])[0]
reversed_precision = np.fliplr([precision])[0]
reversed_mean_precision += interp(mean_recall, reversed_recall, reversed_precision)
reversed_mean_precision[0] = 0.0

And making sure to reverse back when plotting:

reversed_mean_precision /= FOLDS
reversed_mean_precision[0] = 1
mean_auc_pr = auc(mean_recall, reversed_mean_precision)
plt.plot(mean_recall,  np.fliplr([reversed_mean_precision])[0], 'k--',
         label='Mean precision (area = %0.2f)' % mean_auc_pr, lw=2)

The full code here:

FOLDS = 10
AUCs = []
AUCs_proba = []

precision_combined = []
recall_combined = []
thresholds_combined = []

X_ = pred_features.as_matrix()
Y_ = pred_true.as_matrix()

k_fold = cross_validation.KFold(n=len(pred_features), n_folds=FOLDS,shuffle=True,random_state=None)
clf = svm.SVC(kernel='linear', C = 1.0)
mean_tpr = 0.0
mean_fpr = np.linspace(0, 1, 100)
all_tpr = []
reversed_mean_precision = 0.0
mean_recall = np.linspace(0, 1, 100)
all_precision = []

for train_index, test_index in k_fold:
    xtrain, xtest = pred_features.iloc[train_index], pred_features.iloc[test_index]
    ytrain, ytest = pred_true[train_index], pred_true[test_index]
    test_prob = clf.fit(xtrain,ytrain).predict(xtest)
    precision, recall, thresholds = metrics.precision_recall_curve(ytest, test_prob, pos_label=2)
    reversed_recall = np.fliplr([recall])[0]
    reversed_precision = np.fliplr([precision])[0]
    reversed_mean_precision += interp(mean_recall, reversed_recall, reversed_precision)
    reversed_mean_precision[0] = 0.0

    AUCs.append(metrics.auc(recall, precision))

plt.plot([0, 1], [0, 1], '--', color=(0.6, 0.6, 0.6), label='Luck')

reversed_mean_precision /= FOLDS
reversed_mean_precision[0] = 1
mean_auc_pr = auc(mean_recall, reversed_mean_precision)
plt.plot(mean_recall,  np.fliplr([reversed_mean_precision])[0], 'k--',
         label='Mean precision (area = %0.2f)' % mean_auc_pr, lw=2)

plt.xlim([0, 1])
plt.ylim([0, 1])
plt.xlabel('Recall')
plt.ylabel('Precision')
plt.title('Precision Recall')
plt.legend(loc="lower right")
plt.show()
print "AUCs: "
print  sum(AUCs) / float(len(AUCs))