使用DFP算法求解最大熵模型的学习问题用python，加载的手写数据集实现

首先需要导入相关的库：

import numpy as np
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split

然后加载手写数字数据集：

digits = load_digits()
X, y = digits.data, digits.target

接着将数据集划分为训练集和测试集：

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)

定义最大熵模型类：

class MaxEnt:
    def __init__(self, max_iter=100):
        self.max_iter = max_iter
    
    def _init_params(self, X, y):
        self.num_samples, self.num_features = X.shape
        self.num_classes = len(set(y))
        self.X, self.y = X, y
        self.w = np.zeros((self.num_features, self.num_classes))
        self._calcu_feat_list()
    
    def _calcu_feat_list(self):
        self.feat_list = []
        for i in range(self.num_samples):
            feat_dict = {}
            for j in range(self.num_features):
                feat_dict[(j, self.X[i][j])] = feat_dict.get((j, self.X[i][j]), 0) + 1
            self.feat_list.append(feat_dict)
    
    def _calcu_p_y_given_x(self, x):
        prob_list = []
        for i in range(self.num_classes):
            w_i = self.w[:, i]
            prob = np.exp(np.dot(w_i, x)) / sum(np.exp(np.dot(self.w[:, j], x)) for j in range(self.num_classes))
            prob_list.append(prob)
        return prob_list
    
    def train(self, X, y):
        self._init_params(X, y)
        for i in range(self.max_iter):
            error = 0
            for j in range(self.num_samples):
                x = np.zeros(self.num_features)
                for k, v in self.feat_list[j].items():
                    x[k[0]] = v
                
                prob_list = self._calcu_p_y_given_x(x)
                pred_y = np.argmax(prob_list)
                if pred_y != self.y[j]:
                    error += 1
                    for k, v in self.feat_list[j].items():
                        self.w[k[0], self.y[j]] += v
                        self.w[k[0], pred_y] -= v
            if error == 0:
                break
    
    def predict(self, X):
        pred_list = []
        for i in range(len(X)):
            x = X[i]
            prob_list = self._calcu_p_y_given_x(x)
            pred_y = np.argmax(prob_list)
            pred_list.append(pred_y)
        return pred_list

最后实例化类并进行训练和预测：

model = MaxEnt()
model.train(X_train, y_train)
pred_y = model.predict(X_test)

完整代码如下：

import numpy as np
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split

class MaxEnt:
    def __init__(self, max_iter=100):
        self.max_iter = max_iter
    
    def _init_params(self, X, y):
        self.num_samples, self.num_features = X.shape
        self.num_classes = len(set(y))
        self.X, self.y = X, y
        self.w = np.zeros((self.num_features, self.num_classes))
        self._calcu_feat_list()
    
    def _calcu_feat_list(self):
        self.feat_list = []
        for i in range(self.num_samples):
            feat_dict = {}
            for j in range(self.num_features):
                feat_dict[(j, self.X[i][j])] = feat_dict.get((j, self.X[i][j]), 0) + 1
            self.feat_list.append(feat_dict)
    
    def _calcu_p_y_given_x(self, x):
        prob_list = []
        for i in range(self.num_classes):
            w_i = self.w[:, i]
            prob = np.exp(np.dot(w_i, x)) / sum(np.exp(np.dot(self.w[:, j], x)) for j in range(self.num_classes))
            prob_list.append(prob)
        return prob_list
    
    def train(self, X, y):
        self._init_params(X, y)
        for i in range(self.max_iter):
            error = 0
            for j in range(self.num_samples):
                x = np.zeros(self.num_features)
                for k, v in self.feat_list[j].items():
                    x[k[0]] = v
                
                prob_list = self._calcu_p_y_given_x(x)
                pred_y = np.argmax(prob_list)
                if pred_y != self.y[j]:
                    error += 1
                    for k, v in self.feat_list[j].items():
                        self.w[k[0], self.y[j]] += v
                        self.w[k[0], pred_y] -= v
            if error == 0:
                break
    
    def predict(self, X):
        pred_list = []
        for i in range(len(X)):
            x = X[i]
            prob_list = self._calcu_p_y_given_x(x)
            pred_y = np.argmax(prob_list)
            pred_list.append(pred_y)
        return pred_list

digits = load_digits()
X, y = digits.data, digits.target
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)

model = MaxEnt()
model.train(X_train, y_train)
pred_y = model.predict(X_test)

accuracy = sum(pred_y == y_test) / len(y_test)
print('Accuracy:', accuracy)