最大熵模型拟牛顿法用mnist数据集代码

以下是使用最大熵模型拟牛顿法（L-BFGS）对MNIST数据集进行分类的示例代码：

import numpy as np
from scipy.optimize import minimize, fmin_l_bfgs_b
from sklearn.datasets import fetch_openml
from sklearn.preprocessing import LabelBinarizer

# 加载MNIST数据集
mnist = fetch_openml('mnist_784')
X = mnist.data.astype('float64') / 255.0
y = mnist.target.astype('int')

# 将标签进行二元编码
lb = LabelBinarizer()
y_onehot = lb.fit_transform(y)

# 定义最大熵模型的损失函数
def maxent_loss(w, X, y_onehot, C=1.0):
    n_samples, n_features = X.shape
    n_classes = y_onehot.shape[1]
    w = w.reshape((n_features, n_classes))
    scores = np.dot(X, w)
    exp_scores = np.exp(scores)
    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
    loss = -np.sum(y_onehot * np.log(probs)) / n_samples + 0.5 * C * np.sum(w * w)
    grad = np.dot(X.T, probs - y_onehot) / n_samples + C * w
    grad = grad.ravel()
    return loss, grad

# 初始化权重向量
n_features = X.shape[1]
n_classes = y_onehot.shape[1]
w_init = np.zeros((n_features, n_classes))

# 使用L-BFGS来最小化最大熵模型的损失函数
w_opt, f, d = fmin_l_bfgs_b(maxent_loss, w_init.ravel(), args=(X, y_onehot), maxiter=500, factr=1e7)

# 使用训练好的权重向量进行预测
scores = np.dot(X, w_opt.reshape((n_features, n_classes)))
y_pred = np.argmax(scores, axis=1)
accuracy = np.mean(y_pred == y)
print('Accuracy: %.2f%%' % (accuracy * 100))

注意，这里使用了L-BFGS算法来最小化最大熵模型的损失函数。L-BFGS是一种拟牛顿法，可以高效地求解大规模的无约束最优化问题。另外，这里使用了Scipy库中的fmin_l_bfgs_b函数来实现L-BFGS算法。