本文主要是介绍HW2-Logistic regression&Mini-batch gradient descent classfication，对大家解决编程问题具有一定的参考价值，需要的程序猿们随着小编来一起学习吧！

施工中

先按照范例写了用Mini-batch的logistic regression，处理方式和范例有一些区别，因为不太会numpy，只会矩阵向量乘来乘去，不会用广播之类的操作(((

如果仿照范例不做优化的话，在train_set上跑出来的acc和loss和范例差不多

Preprocess

import numpy as np

with open("./X_train") as f:
    next(f)
    X_train = np.array([line.strip('\n').split(',')[1:] for line in f], dtype = float)

with open("./Y_train") as f:
    next(f)
    # 和范例不同，这里读进来的是列向量
    Y_train = np.array([line.strip('\n').split(',')[1:] for line in f], dtype = float)

with open("./X_test") as f:
    next(f)
    X_test = np.array([line.strip('\n').split(',')[1:] for line in f], dtype = float)

Normalize

\(X_{after} = \frac{X - X_{mean}}{\sigma}\)

# 算出train_set的mean和std
X_mean = np.mean(X_train[:,range(X_train.shape[1])], axis = 0).flatten()
X_std = np.std(X_train[:,range(X_train.shape[1])], axis = 0).flatten()
# 对X_train进行Normalize
X_train[:,range(X_train.shape[1])] = (X_train[:,range(X_train.shape[1])]-X_mean)/(X_std + 1e-8)
# 同理
X_test[:,range(X_test.shape[1])] = (X_test[:,range(X_test.shape[1])]-X_mean)/(X_std+1e-8)

Train dev split

划分出train_set and development_set

dev_ratio = 0.1 # development_set占比
train_size = int((1 - dev_ratio) * len(X_train))
X_dev = X_train[train_size:]
Y_dev = Y_train[train_size:]
X_train = X_train[:train_size]
Y_train = Y_train[:train_size]

Function(shuffle、logistic、sigmoid、cross_entropy......)

# 洗牌
np.random.seed(0)
def _shuffle(X, Y):
    randomize = np.arange(len(X)) # 得到长度为len(x)的多个0的permutation
    np.random.shuffle(randomize) # 将排列打乱
    return X[randomize], Y[randomize] # 把X和Y用这个排列作为索引打乱


# sigmoid函数
def _sigmoid(z):
    return np.clip(1 / (1.0 + np.exp(-z)), 1e-8, 1-(1e-8)) # 规定作为边界最大值和最小值，超过限度的值都会取边界


# 得到一组x和w logistic回归的结果
# X: input data
# w: weight vector
# b: bais
def _f(X, w, b):
    return _sigmoid(np.dot(X, w) + b)

# 得到二分类结果
def _predict(X, w, b):
    return np.round(_f(X, w, b)).astype(np.int)


# acc
def _accuracy(Y_pred, Y_label):
    return 1 - np.mean(np.abs(Y_pred - Y_label))

# 交叉熵 = - yhat * ln(f(x_n)) - (1 - yhat) * ln(1 - f(x_n))
# 将cross_entropy求和得到损失
def _cross_entropy_loss(Y_pred, Y_label):
    cross_entropy = -np.dot(Y_label.transpose(), np.log(Y_pred)) - np.dot(1 - Y_label.transpose(), np.log(1 - Y_pred))
    #print(cross_entropy)
    return cross_entropy[0][0]

# 梯度 w_grad = -\sigma {(yhat - f(x_n)) * X.T}, b_grad = -\sigma {(yhat - f(x_n))}
def _gradient(X, Y_label, w, b):
    #print(Y_label.flatten())
    #print(_f(X, w, b).flatten())
    pred_error = (Y_label.flatten() - _f(X, w, b).flatten()) # 得到行向量
    #print(Y_pred)
    #print(Y_label)
    #print(pred_error)
    #print(pred_error.shape)
    #print(X)
    #print(np.sum(np.dot(pred_error, X)))
    w_grad = -np.dot(pred_error, X) # 让它对X的每一维求内积得到行向量w_grad
    b_grad = -np.sum(pred_error) # 对b求微分的结果就是pred_error求和
    #print(w_grad.shape)
    return w_grad.reshape(X_train.shape[1],1), b_grad # 返回列向量

Training

# 初始化参数
w = np.zeros((X_train.shape[1],1))
b = np.zeros((1,))

print(w.shape)
print(b)

max_iter = 10 # 迭代次数
batch_size = 10 # mini-batch每次选取的size
learning_rate = 0.25

train_loss = []
dev_loss = []
train_acc = []
dev_acc = []

cnt = 1 # 下降的步数，用于每一步后调整学习率


for epoch in range(max_iter):
    X_train, Y_train = _shuffle(X_train, Y_train)
    
    # Mini-batch training
    for idx in range(train_size//batch_size):
        X = X_train[idx*batch_size:(idx+1)*batch_size]
        Y = Y_train[idx*batch_size:(idx+1)*batch_size]
        #print(X.shape)
        #print(Y.shape)
        # 计算梯度
        w_grad, b_grad = _gradient(X, Y, w, b)
        
        w = w - learning_rate/np.sqrt(cnt) * w_grad
        #print(w)
        b = b - learning_rate/np.sqrt(cnt) * b_grad
        cnt += 1
        #print(cnt)
    
    # 计算acc和平均loss
    Y_train_pred = np.round(_f(X_train, w, b))
    train_acc.append(_accuracy(Y_train_pred, Y_train))
    #print(_cross_entropy_loss(_f(X_train, w, b), Y_train))
    #print("\n\n")
    train_loss.append(_cross_entropy_loss(_f(X_train, w, b), Y_train)/len(X_train))
    
    Y_dev_pred = np.round(_f(X_dev, w, b))
    dev_acc.append(_accuracy(Y_dev_pred, Y_dev))
    dev_loss.append(_cross_entropy_loss(_f(X_dev, w, b), Y_dev)/len(X_dev))
    print(train_loss[-1])
    #print("\n")
    print(train_acc[-1])
print('Training loss: {}'.format(train_loss[-1]))
print('Development loss: {}'.format(dev_loss[-1]))
print('Training accuracy: {}'.format(train_acc[-1]))
print('Development accuracy: {}'.format(dev_acc[-1]))

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