Python实现计算AUC的三种方式总结

目录

• 介绍
• 实现代码
• 方法补充

介绍

AUC（Area Under Curve）被定义为ROC曲线下与坐标轴围成的面积，显然这个面积的数值不会大于1。又由于ROC曲线一般都处于y=x这条直线的上方，所以AUC的取值范围在0.5和1之间。AUC越接近1.0，检测方法真实性越高;等于0.5时，则真实性最低，无应用价值。

auc计算方式：参考Python实现计算AUC的示例代码

实现代码

import numpy as np
from sklearn.metrics import roc_auc_score
y_true = [1,1,0,0,1,1,0]
y_pred = [0.8,0.7,0.5,0.5,0.5,0.5,0.3]
print(roc_auc_score(y_true, y_pred))
# 下面实现的是方法1
# https://blog.csdn.net/lieyingkub99/article/details/81266664?utm_medium=distribute.pc_relevant.none-task-blog-title-1&spm=1001.2101.3001.4242
def cal_auc1(y_true, y_pred):
    n_bins = 10
    postive_len = sum(y_true)  # M正样本个数
    negative_len = len(y_true) - postive_len  # N负样本个数
    total_case = postive_len * negative_len  # M * N样本对数
    pos_histogram = [0 for _ in range(n_bins)]  # 保存每一个概率值下的正样本个数
    neg_histogram = [0 for _ in range(n_bins)]  # 保存每一个概率值下的负样本个数
    bin_width = 1.0 / n_bins
    for i in range(len(y_true)):
        nth_bin = int(y_pred[i] / bin_width)  # 概率值转化为整数下标
        if y_true[i] == 1:
            pos_histogram[nth_bin] += 1
        else:
            neg_histogram[nth_bin] += 1
    print(pos_histogram)
    print(neg_histogram)
    accumulated_neg = 0
    satisfied_pair = 0
    for i in range(n_bins):
        satisfied_pair += (pos_histogram[i] * accumulated_neg + pos_histogram[i] * neg_histogram[i] * 0.5)
        print(pos_histogram[i], neg_histogram[i], accumulated_neg, satisfied_pair)
        accumulated_neg += neg_histogram[i]

    return satisfied_pair / float(total_case)
print(cal_auc1(y_true, y_pred))
# 下面实现的是方法2
# https://blog.csdn.net/lieyingkub99/article/details/81266664?utm_medium=distribute.pc_relevant.none-task-blog-title-1&spm=1001.2101.3001.4242
def cal_auc2(y_true, y_pred):
    n_bins = 10
    postive_len = sum(y_true)  # M正样本个数
    negative_len = len(y_true) - postive_len  # N负样本个数
    total_case = postive_len * negative_len  # M * N样本对数
    prob_rank = [0 for _ in range(n_bins)]  # 保存每一个概率值的rank
    prob_num = [0 for _ in range(n_bins)]  # 保存每一个概率值出现的次数
    bin_width = 1.0 / n_bins
    raw_arr = []
    for i in range(len(y_true)):
        raw_arr.append([y_pred[i], y_true[i]])
    arr = sorted(raw_arr, key=lambda d: d[0]) # 按概率由低到高排序
    for i in range(len(arr)):
        nth_bin = int(arr[i][0] / bin_width)  # 概率值转化为整数下标
        prob_rank[nth_bin] = prob_rank[nth_bin] + i + 1
        prob_num[nth_bin] = prob_num[nth_bin] + 1
    satisfied_pair = 0
    for i in range(len(arr)):
        if arr[i][1] == 1:
            nth_bin = int(arr[i][0] / bin_width)  # 概率值转化为整数下标
            satisfied_pair = satisfied_pair + prob_rank[nth_bin] / prob_num[nth_bin]
    return (satisfied_pair - postive_len * (postive_len + 1) / 2 ) / total_case

print(cal_auc2(y_true, y_pred))

# 根据roc曲线,找不同点算下面积, 需要点足够多
def cal_auc3(y_true, y_pred):
    """Summary
    Args:
        raw_arr (TYPE): Description
    Returns:
        TYPE: Description
    """
    raw_arr = []
    for i in range(len(y_true)):
        raw_arr.append([y_pred[i], y_true[i]])
    print(raw_arr)
    arr = sorted(raw_arr, key=lambda d:d[0], reverse=True)
    pos, neg = 0., 0.
    for record in arr:
        if record[1] == 1.:
            pos += 1
        else:
            neg += 1

    fp, tp = 0., 0.
    xy_arr = []
    for record in arr:
        if record[1] == 1.:
            tp += 1
        else:
            fp += 1
        xy_arr.append([fp/neg, tp/pos])
    print(xy_arr)
    auc = 0.
    prev_x = 0.
    prev_y = 0.
    for x, y in xy_arr:
        if x != prev_x:
            auc += ((x - prev_x) * (y + prev_y) / 2.)
            prev_x = x
            prev_y = y
        print(auc)
    import numpy as np
    from sklearn.metrics import roc_auc_score
    y_true = [1, 1, 0, 0, 1, 1, 0]
    y_pred = [0.8, 0.7, 0.5, 0.5, 0.5, 0.5, 0.3]
    print(roc_auc_score(y_true, y_pred))

方法补充

下面是小编为大家找到的另外三个计算AUC的代码，会输出三种方法各自的auc，以及通过面积计算AUC时的ROC曲线。

在通过面积计算AUC的方法中，没有遍历数据的预测概率作为分类阈值，而是对[0,1]区间等分得到一系列阈值。

# AUC的计算
import numpy as np
import matplotlib.pyplot as plt

for e in range(3):
    print("\nRound: ", e+1)

    num = 1000
    auc1 = auc2 = auc3 = 0.

    # 准备数据
    pred_prob = list(np.random.uniform(low=0,high=1, size=[num]))
    labels = [int(prob>0.5) for prob in list(np.random.uniform(low=0,high=1, size=[num]))]

    # 检查数据
    # print("pred_prob:\n", pred_prob)
    # print("labels:\n", labels)

    # 方法一，面积加和
    roc_point = []
    for i in range(num):
        i = pred_prob[i]
        TP = 0  # 真阳样本数
        FP = 0  # 假阳样本数
        TP_rate = 0.  # 真阳率
        FP_rate = 0.  # 假阳率
        pos_num = 0   # 预测真样本数

        # 计数过程
        for ind, prob in enumerate(pred_prob):
            if prob>i:
                pos_num += 1
            if prob>i and labels[ind]>0.5:
                TP+=1
            elif prob>i and labels[ind]<0.5:
                FP+=1
        if pos_num!=0:
            TP_rate = TP / sum(labels)
            FP_rate = FP / (num-sum(labels))
        roc_point.append([FP_rate, TP_rate])  # 记录ROC中的点
    # 画出ROC曲线
    roc_point.sort(key=lambda x: x[0])
    plt.plot(np.array(roc_point)[1:, 0], np.array(roc_point)[1: ,1])
    plt.xlabel("FPR")
    plt.ylabel("TPR")
    plt.show()

    # 计算每个小长方形的面积，求和即为auc
    lastx = 0.
    for x,y in roc_point:
        auc1 += (x-lastx)*y  # 底乘高
        lastx = x

    print("方法一 auc:", auc1)

    # 方法二，利用AUC关于排列概率的定义计算
    auc2 = 0
    P_ind = []  # 正样本下标
    F_ind = []  # 负样本下标
    P_F = 0  # 正样本分数高于负样本的数量
    F_P = 0  # 负样本分数高于正样本的数量

    #  计数过程
    for ind, val in enumerate(labels):
        if val > 0.5:
            P_ind.append(ind)
        else:
            F_ind.append(ind)
    for Pi in P_ind:
        for Fi in F_ind:
            if pred_prob[Pi] > pred_prob[Fi]:
                P_F += 1
            else:
                F_P += 1
    auc2 = P_F/(len(P_ind)*len(F_ind))
    print("方法二 auc:", auc2)

    # 方法三，方法二的改进，简化了计算，降低了时间复杂度
    new_data = [[p, l] for p, l in zip(pred_prob, labels)]
    new_data.sort(key=lambda x:x[0])

    # 求正样本rank之和
    rank_sum = 0
    for ind, [prob,label] in enumerate(new_data):
        if label>0.5:
            rank_sum+=ind
    auc3 = (rank_sum - len(P_ind)*(1+len(P_ind))/2) / (len(P_ind)*len(F_ind))
    print("方法三 auc:", auc3)

运行结果

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