朴素贝叶斯分类器

朴素贝叶斯法是基于贝叶斯定理与特征条件独立假设的分类方法。对于输入数据集，首先基于特征条件独立假设学习输入/输出的联合概率分布，然后基于此模型对给定的输入x，利用贝叶斯定理求出后验概率最大的输出y。

进一步学习：

朴素贝叶斯分类器

  • 四种实现方式：自己实现、高斯贝叶斯模型、伯努利模型、多项式模型
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import numpy as np
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import pandas as pd
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from sklearn.datasets import load_iris
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from sklearn.model_selection import train_test_split
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import math
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# 加载数据
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def load_data():
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    iris = load_iris()
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    df = pd.DataFrame(iris.data, columns=iris.feature_names)
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    df['label'] = iris.target
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    df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label']
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    data = np.array(df.iloc[:100, :])
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    return data[:, :-1], data[:, -1]
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# 朴素贝叶斯分类器
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class NaiveBayes:
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    def __init__(self):
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        self.model = None
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    # 数学期望
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    def mean(self, X):
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        return sum(X) / float(len(X))
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    # 标准差
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    def stdev(self, X):
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        avg = self.mean(X)
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        return math.sqrt(sum([pow(x-avg, 2) for x in X]) / float(len(X)))
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    # 高斯概率密度函数
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    def gaussian_probability(self, x, mean, stdev):
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        exponent = math.exp(-(math.pow(x-mean, 2)/(2*math.pow(stdev, 2))))
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        return (1 / (math.sqrt(2*math.pi) * stdev)) * exponent
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    # 处理X_train
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    def summarize(self, train_data):
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        summaries = [(self.mean(i), self.stdev(i)) for i in zip(*train_data)]
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        return summaries
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    # 分类别求出数学期望和标准差
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    def fit(self, X, y):
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        labels = list(set(y))
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        data = {label: [] for label in labels}
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        for f, label in zip(X, y):
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            data[label].append(f)
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        self.model = {label: self.summarize(value) for label, value in data.items()}
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        return 'GaussianNB train done!'
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    # 计算概率
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    def calculate_probabilities(self, input_data):
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        # summaries:{0.0: [(5.0, 0.37),(3.42, 0.40)], 1.0: [(5.8, 0.449),(2.7, 0.27)]}
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        # input_data:[1.1, 2.2]
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        probabilities = {}
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        for label, value in self.model.items():
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            probabilities[label] = 1
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            for i in range(len(value)):
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                mean, stdev = value[i]
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                probabilities[label] *= self.gaussian_probability(input_data[i], mean, stdev)
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        return probabilities
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    # 预测类别
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    def predict(self, X_test):
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        # {0.0: 2.9680340789325763e-27, 1.0: 3.5749783019849535e-26}
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        label = sorted(self.calculate_probabilities(X_test).items(), key=lambda x: x[-1])[-1][0]
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        return label
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    # 评价模型
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    def score(self, X_test, y_test):
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        right = 0
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        for X, y in zip(X_test, y_test):
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            label = self.predict(X)
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            if label == y:
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                right += 1
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        return right / float(len(X_test))
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if __name__ == '__main__':
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    # 加载数据
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    X, y = load_data()
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    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)
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    # 自己实现NaiveBayes分类器
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    print('My NaiveBayes')
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    model = NaiveBayes()
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    model.fit(X_train, y_train)
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    one_example = [4.4, 3.2, 1.3, 0.2]
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    print('The label of [4.4, 3.2, 1.3, 0.2] is: ' + str(model.predict(one_example)))
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    print('Accuracy in test data set: ' + str(model.score(X_test, y_test)))
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    print()
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    # sklearn库中的NaiveBayes分类器
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    from sklearn.naive_bayes import GaussianNB  # 高斯贝叶斯模型
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    print("Sklearn's GaussianNB")
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    clf = GaussianNB()
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    clf.fit(X_train, y_train)
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    print('The label of [4.4, 3.2, 1.3, 0.2] is: ' + str(clf.predict([[4.4, 3.2, 1.3, 0.2]])))
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    print('Accuracy in test data set: ' + str(clf.score(X_test, y_test)))
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    print()
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    from sklearn.naive_bayes import BernoulliNB  # 伯努利模型
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    print("Sklearn's BernoulliNB")
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    clf = BernoulliNB()
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    clf.fit(X_train, y_train)
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    print('The label of [4.4, 3.2, 1.3, 0.2] is: ' + str(clf.predict([[4.4, 3.2, 1.3, 0.2]])))
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    print('Accuracy in test data set: ' + str(clf.score(X_test, y_test)))
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    print()
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    from sklearn.naive_bayes import MultinomialNB  # 多项式模型
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    print("Sklearn's MultinomialNB")
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    clf = MultinomialNB()
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    clf.fit(X_train, y_train)
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    print('The label of [4.4, 3.2, 1.3, 0.2] is: ' + str(clf.predict([[4.4, 3.2, 1.3, 0.2]])))
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    print('Accuracy in test data set: ' + str(clf.score(X_test, y_test)))
  • 实验结果
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My NaiveBayes
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The label of [4.4, 3.2, 1.3, 0.2] is: 0.0
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Accuracy in test data set: 1.0
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GaussianNB in sklearn
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The label of [4.4, 3.2, 1.3, 0.2] is: [0.]
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Accuracy in test data set: 1.0
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BernoulliNB in sklearn
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The label of [4.4, 3.2, 1.3, 0.2] is: [0.]
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Accuracy in test data set: 0.4666666666666667
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MultinomialNB in sklearn
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The label of [4.4, 3.2, 1.3, 0.2] is: [0.]
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Accuracy in test data set: 1.0