基于最大熵原理的贝叶斯评定python代码

首先，最大熵原理是一种求解概率分布的方法，而贝叶斯评定是一种分类的方法，两者并不直接相关。但是可以基于最大熵原理来构建分类模型，然后使用贝叶斯评定来进行分类。

下面给出一个基于最大熵原理构建分类模型的Python代码，并使用贝叶斯评定来进行评估：

import numpy as np
from collections import defaultdict
from scipy.optimize import minimize
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

class MaxEntropy:

    def __init__(self, epsilon=1e-5, max_iteration=1000):
        self.epsilon = epsilon
        self.max_iteration = max_iteration

    def fit(self, X, y):
        self.labels = list(set(y))
        self.feature2id = defaultdict(lambda: len(self.feature2id))
        self.id2feature = {v: k for k, v in self.feature2id.items()}
        self.n_features = len(self.feature2id)
        self.n_labels = len(self.labels)
        self.X = self.transform(X)
        self.y = np.array(y)
        self.w = np.zeros(self.n_features)
        self._train()

    def transform(self, X):
        n_samples = X.shape[0]
        X_new = []
        for i in range(n_samples):
            x = X[i]
            x_new = [0] * self.n_features
            for j in range(len(x)):
                if x[j] in self.feature2id:
                    x_new[self.feature2id[x[j]]] = 1
            X_new.append(x_new)
        return np.array(X_new)

    def _train(self):
        n_samples = self.X.shape[0]
        for iteration in range(self.max_iteration):
            w_old = np.copy(self.w)
            for i in range(n_samples):
                x = self.X[i]
                y = self.y[i]
                p = self.predict_proba(x)
                for j in range(self.n_features):
                    self.w[j] += self.epsilon * (self.expected_feature_value(j, x, y) - self.expected_feature_value(j, x, p))
            if np.sum(np.abs(self.w - w_old)) < self.epsilon:
                break

    def predict_proba(self, x):
        p = np.zeros(self.n_labels)
        for y in range(self.n_labels):
            s = np.dot(self.w, self.feature_value(x, y))
            p[y] = np.exp(s)
        p /= np.sum(p)
        return p

    def predict(self, X):
        X_new = self.transform(X)
        y_pred = []
        for i in range(X_new.shape[0]):
            p = self.predict_proba(X_new[i])
            y_pred.append(self.labels[np.argmax(p)])
        return y_pred

    def feature_value(self, x, y):
        f = np.zeros(self.n_features)
        for i in range(len(x)):
            if x[i] in self.feature2id:
                f[self.feature2id[x[i]]] = int(y == self.labels.index(x[i]))
        return f

    def expected_feature_value(self, j, x, y):
        p = self.predict_proba(x)
        f = self.feature_value(x, y)
        return np.dot(f, p) - self.expected_feature_value(j, x, p)

if __name__ == '__main__':
    # 生成模拟数据
    X = [['sunny', 'hot'], ['sunny', 'cool'], ['overcast', 'hot'], ['rainy', 'mild'], ['rainy', 'cool'], ['overcast', 'cool']]
    y = ['no', 'yes', 'yes', 'yes', 'no', 'yes']

    # 划分数据集
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

    # 训练模型
    model = MaxEntropy()
    model.fit(X_train, y_train)

    # 预测结果
    y_pred = model.predict(X_test)

    # 评估模型
    accuracy = accuracy_score(y_test, y_pred)
    print('Accuracy:', accuracy)

上述代码中使用了一个简单的数据集，包含6个样本，每个样本有2个特征，共有2个类别。使用最大熵原理构建了一个分类模型，并使用贝叶斯评定进行评估。