梯度下降求解逻辑回归（代码）

import numpy as npimport pandas as pdimport matplotlib.pyplot as plt%matplotlib inlineimport ospath = 'data' + os.sep + 'LogiReg_data.txt'pdData = pd.read_csv(path, header=None, names=['Exam 1', 'Exam 2', 'Admitted'])pdData.head()#前两列为特征，第三列为录取与否pdData.shape#100个数据，每个样本有三列特征值positive = pdData[pdData['Admitted'] == 1]#正例，返回行子集negative = pdData[pdData['Admitted'] == 0]#负例（进行指定）fig,ax = plt.subplots(figsize=(10,15))#figsize为画图域，长15，宽10ax.scatter(positive['Exam 1'], positive['Exam 2'], s=30, c='b', marker='o', label='Admitted')#正例和负例，标签与颜色ax.scatter(negative['Exam 1'], negative['Exam 2'], s=30, c='r', marker='x', label='Not Admitted')ax.legend()ax.set_xlabel('Exam 1 Score')ax.set_ylabel('Exam 2 Score')def sigmoid(z):#定义sigmod函数    return 1 / (1 + np.exp(-z))#np.exp(-z)为e的-z次幂（转数值运算为矩阵运算）nums = np.arange(-10, 10, step=1) #creates a vector containing 20 equally spaced values from -10 to 10fig, ax = plt.subplots(figsize=(12,4))ax.plot(nums, sigmoid(nums), 'r')def model(X, theta):#输入X数域，theta为参数（model为预测函数）        return sigmoid(np.dot(X, theta.T))#np.dot为矩阵乘法，X与theta相乘，结果传入sigmod函数中pdData.insert(0, 'Ones', 1) # 新加一列，列名为Ones，值全为1# set X (training data) and y (target variable)orig_data = pdData.as_matrix() # convert the Pandas representation of the data to an array useful for further computationscols = orig_data.shape[1]X = orig_data[:,0:cols-1]y = orig_data[:,cols-1:cols]# convert to numpy arrays and initalize the parameter array theta#X = np.matrix(X.values)#y = np.matrix(data.iloc[:,3:4].values) #np.array(y.values)theta = np.zeros([1, 3])#构造1行三列的theta参数，占位X[:5]y[:5]thetaX.shape, y.shape, theta.shapedef cost(X, y, theta):#定义损失函数，X为数据，y为标签，theta为参数    left = np.multiply(-y, np.log(model(X, theta)))    right = np.multiply(1 - y, np.log(1 - model(X, theta)))    return np.sum(left - right) / (len(X))cost(X, y, theta)def gradient(X, y, theta):    grad = np.zeros(theta.shape)#定义梯度，与theta一一对应    error = (model(X, theta)- y).ravel()    for j in range(len(theta.ravel())): #for each parmeter        term = np.multiply(error, X[:,j])#取第j列样本        grad[0, j] = np.sum(term) / len(X)        return gradSTOP_ITER = 0STOP_COST = 1STOP_GRAD = 2def stopCriterion(type, value, threshold):    #设定三种不同的停止策略    if type == STOP_ITER:        return value > threshold  #指定次数    elif type == STOP_COST:      return abs(value[-1]-value[-2]) < threshold #指定阈值    elif type == STOP_GRAD:      return np.linalg.norm(value) < threshold  #指定阈值import numpy.random#洗牌def shuffleData(data):    np.random.shuffle(data)    cols = data.shape[1]    X = data[:, 0:cols-1]    y = data[:, cols-1:]    return X, yimport time#观察时间对结果的影响def descent(data, theta, batchSize, stopType, thresh, alpha):#数据，参数，梯度下降样式，策略，阈值，学习率    #梯度下降求解        init_time = time.time()    i = 0 # 迭代次数    k = 0 # batch    X, y = shuffleData(data)    grad = np.zeros(theta.shape) # 计算的梯度    costs = [cost(X, y, theta)] # 损失值        while True:        grad = gradient(X[k:k+batchSize], y[k:k+batchSize], theta)        k += batchSize #取batch数量个数据        if k >= n:             k = 0             X, y = shuffleData(data) #重新洗牌        theta = theta - alpha*grad # 参数更新        costs.append(cost(X, y, theta)) # 计算新的损失        i += 1         if stopType == STOP_ITER:       value = i        elif stopType == STOP_COST:     value = costs        elif stopType == STOP_GRAD:     value = grad        if stopCriterion(stopType, value, thresh): break        return theta, i-1, costs, grad, time.time() - init_time def runExpe(data, theta, batchSize, stopType, thresh, alpha):#根据参数选择梯度下降方式和策略    #import pdb; pdb.set_trace();    theta, iter, costs, grad, dur = descent(data, theta, batchSize, stopType, thresh, alpha)    name = "Original" if (data[:,1]>2).sum() > 1 else "Scaled"    name += " data - learning rate: {} - ".format(alpha)    if batchSize==n: strDescType = "Gradient"    elif batchSize==1:  strDescType = "Stochastic"    else: strDescType = "Mini-batch ({})".format(batchSize)    name += strDescType + " descent - Stop: "    if stopType == STOP_ITER: strStop = "{} iterations".format(thresh)    elif stopType == STOP_COST: strStop = "costs change < {}".format(thresh)    else: strStop = "gradient norm < {}".format(thresh)    name += strStop    print ("***{}\nTheta: {} - Iter: {} - Last cost: {:03.2f} - Duration: {:03.2f}s".format(        name, theta, iter, costs[-1], dur))    fig, ax = plt.subplots(figsize=(12,4))    ax.plot(np.arange(len(costs)), costs, 'r')    ax.set_xlabel('Iterations')    ax.set_ylabel('Cost')    ax.set_title(name.upper() + ' - Error vs. Iteration')    return theta#选择的梯度下降方法是基于所有样本的n=100runExpe(orig_data, theta, n, STOP_ITER, thresh=5000, alpha=0.000001)runExpe(orig_data, theta, n, STOP_COST, thresh=0.000001, alpha=0.001)runExpe(orig_data, theta, n, STOP_GRAD, thresh=0.05, alpha=0.001)runExpe(orig_data, theta, 1, STOP_ITER, thresh=5000, alpha=0.001)runExpe(orig_data, theta, 1, STOP_ITER, thresh=15000, alpha=0.000002)runExpe(orig_data, theta, 16, STOP_ITER, thresh=15000, alpha=0.001)from sklearn import preprocessing as ppscaled_data = orig_data.copy()scaled_data[:, 1:3] = pp.scale(orig_data[:, 1:3])runExpe(scaled_data, theta, n, STOP_ITER, thresh=5000, alpha=0.001)runExpe(scaled_data, theta, n, STOP_GRAD, thresh=0.02, alpha=0.001)theta = runExpe(scaled_data, theta, 1, STOP_GRAD, thresh=0.002/5, alpha=0.001)runExpe(scaled_data, theta, 16, STOP_GRAD, thresh=0.002*2, alpha=0.001)#设定阈值def predict(X, theta):    return [1 if x >= 0.5 else 0 for x in model(X, theta)]scaled_X = scaled_data[:, :3]y = scaled_data[:, 3]predictions = predict(scaled_X, theta)correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y)]accuracy = (sum(map(int, correct)) % len(correct))print ('accuracy = {0}%'.format(accuracy))#进行逻辑回归，梯度下降，并对比