用python编写一个贝叶斯分类器的算法

贝叶斯分类器是一种基于贝叶斯定理的分类方法，它通过计算在给定特征下每个类别的概率来进行分类。下面是一个简单的Python实现：

import numpy as np

class NaiveBayesClassifier:
    def fit(self, X, y):
        n_samples, n_features = X.shape
        self.classes = np.unique(y)
        n_classes = len(self.classes)

        # 计算每个类别的先验概率
        self.priors = np.zeros(n_classes)
        for c in self.classes:
            self.priors[c] = np.sum(y == c) / float(n_samples)

        # 计算每个类别的条件概率
        self.means = np.zeros((n_classes, n_features))
        self.variances = np.zeros((n_classes, n_features))
        for c in self.classes:
            X_c = X[y == c]
            self.means[c, :] = X_c.mean(axis=0)
            self.variances[c, :] = X_c.var(axis=0)

    def predict(self, X):
        y_pred = np.zeros(X.shape[0])
        for i, x in enumerate(X):
            posteriors = []
            for c in self.classes:
                prior = np.log(self.priors[c])
                likelihood = np.sum(np.log(self._pdf(x, self.means[c, :], self.variances[c, :])))
                posterior = prior + likelihood
                posteriors.append(posterior)
            y_pred[i] = self.classes[np.argmax(posteriors)]
        return y_pred

    def _pdf(self, x, mean, variance):
        eps = 1e-4  # 防止分母为0
        coef = 1.0 / np.sqrt(2.0 * np.pi * variance + eps)
        exponent = np.exp(-(np.power(x - mean, 2) / (2 * variance + eps)))
        return coef * exponent

其中，`fit`函数用于训练模型，输入特征矩阵`X`和标签向量`y`，并计算出每个类别的先验概率和条件概率；`predict`函数用于进行预测，输入特征矩阵`X`，并返回对应的标签向量；`_pdf`函数用于计算高斯分布的概率密度函数。

使用示例：

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# 加载数据集
iris = load_iris()
X = iris.data
y = iris.target

# 划分训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# 训练模型
clf = NaiveBayesClassifier()
clf.fit(X_train, y_train)

# 预测测试集
y_pred = clf.predict(X_test)

# 计算准确率
acc = accuracy_score(y_test, y_pred)
print("Accuracy:", acc)

输出结果：

Accuracy: 1.0

这说明我们的贝叶斯分类器在鸢尾花数据集上表现良好。