实现简单的sgd算法应用

以下是一个简单的SGD算法应用，假设我们有一个二分类问题，需要通过SGD算法训练一个逻辑回归模型来对样本进行分类。

首先，我们可以使用sklearn库生成随机样本数据：

from sklearn.datasets import make_classification

X, y = make_classification(n_samples=1000, n_features=10, n_classes=2, random_state=42)

接下来，我们可以使用train_test_split函数将数据划分为训练集和测试集：

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

然后，我们可以定义逻辑回归模型的损失函数和梯度函数，并使用SGD算法进行模型训练：

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def loss_fn(w, b, X, y):
    y_pred = sigmoid(np.dot(X, w) + b)
    loss = -(np.mean(y * np.log(y_pred) + (1 - y) * np.log(1 - y_pred)))
    return loss

def grad_fn(w, b, X, y):
    y_pred = sigmoid(np.dot(X, w) + b)
    grad_w = np.dot(X.T, (y_pred - y)) / len(y)
    grad_b = np.mean(y_pred - y)
    return grad_w, grad_b

def sgd(X, y, lr=0.01, batch_size=32, epochs=100):
    n, m = X.shape
    w = np.zeros(m)
    b = 0.0
    for epoch in range(epochs):
        indices = np.random.permutation(n)
        for i in range(0, n, batch_size):
            X_batch = X[indices[i:i+batch_size]]
            y_batch = y[indices[i:i+batch_size]]
            grad_w, grad_b = grad_fn(w, b, X_batch, y_batch)
            w -= lr * grad_w
            b -= lr * grad_b
        loss = loss_fn(w, b, X, y)
        print('Epoch %d, Loss %.4f' % (epoch+1, loss))
    return w, b

最后，我们可以使用训练好的模型对测试集进行预测，并计算预测准确率：

w, b = sgd(X_train, y_train, lr=0.01, batch_size=32, epochs=100)
y_pred = np.round(sigmoid(np.dot(X_test, w) + b))
accuracy = np.mean(y_pred == y_test)
print('Accuracy:', accuracy)

通过适当调节学习率、批量大小和迭代次数等参数，可以得到较好的分类效果。