最大熵模型 IIS / DFP 算法代码实现

以下是最大熵模型的 IIS/DFP 算法的 Python 代码实现：

import numpy as np

class MaxEnt():
    def __init__(self, X, Y):
        self.X = X
        self.Y = Y
        self.N = len(X)
        self.M = len(X[0])
        self.build_dict()
        self.w = np.zeros(self.feature_num)
        self.calcu_Z()

    def build_dict(self):
        self.feat_dict = {}
        idx = 0
        for i in range(self.N):
            for j in range(self.M):
                feat = str(j) + '=' + str(self.X[i][j]) + ',' + str(Y[i])
                if feat not in self.feat_dict:
                    self.feat_dict[feat] = idx
                    idx += 1
        self.feature_num = idx

    def calcu_Z(self):
        self.Z = 0
        for i in range(self.N):
            sum_f = 0
            for j in range(self.M):
                f = str(j) + '=' + str(self.X[i][j]) + ',' + str(self.Y[i])
                if f in self.feat_dict:
                    sum_f += self.w[self.feat_dict[f]]
            self.Z += np.exp(sum_f)

    def calcu_px(self, X):
        sum_f = 0
        for j in range(self.M):
            f = str(j) + '=' + str(X[j]) + ',' + str(0)
            if f in self.feat_dict:
                sum_f += self.w[self.feat_dict[f]]
        px = np.exp(sum_f) / self.Z
        return px

    def calcu_Epfi(self):
        Epfi = np.zeros(self.feature_num)
        for i in range(self.N):
            pxy = self.calcu_px(self.X[i])
            for j in range(self.M):
                f = str(j) + '=' + str(self.X[i][j]) + ',' + str(self.Y[i])
                if f in self.feat_dict:
                    Epfi[self.feat_dict[f]] += pxy
        return Epfi / self.N

    def train(self, max_iter=1000, tol=1e-5):
        for it in range(max_iter):
            w_old = np.copy(self.w)
            Epfi = self.calcu_Epfi()
            for i in range(self.feature_num):
                delta = 1.0 / self.N * np.log(self.Z) - Epfi[i]
                self.w[i] += delta
            self.calcu_Z()
            diff = np.sum(np.abs(self.w - w_old))
            if diff < tol:
                break

    def predict(self, X):
        px = self.calcu_px(X)
        py = np.zeros(2)
        for i in range(2):
            sum_f = 0
            for j in range(self.M):
                f = str(j) + '=' + str(X[j]) + ',' + str(i)
                if f in self.feat_dict:
                    sum_f += self.w[self.feat_dict[f]]
            py[i] = np.exp(sum_f) / self.Z
        return np.argmax(py), px

其中，X 和 Y 分别为训练集的特征和标签，feature_num 表示特征的数量，w 是特征的权重，Z 表示归一化因子。calcu_Z 函数和 calcu_px 函数分别计算归一化因子和某个样本的概率值。calcu_Epfi 函数计算经验期望。train 函数使用 IIS/DFP 算法进行模型训练。predict 函数根据模型预测输入样本的标签和概率值。