求解逻辑回归—-梯度下降

theta = theta - alpha*grad # 参数更新
costs.append(costFunction(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

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, y

def runExpe(data, theta, batchSize, stopType, thresh, alpha):
    #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=100
runExpe(orig_data, theta, n, STOP_ITER, thresh=5000, alpha=0.000001)

***Original data - learning rate: 1e-06 - Gradient descent - Stop: 5000 iterations
Theta: [[-0.00026672] [ 0.00668449] [ 0.00450233]] - Iter: 5000 - Last cost: 0.63 - Duration: 0.95s
array([[-0.00026672],
       [ 0.00668449],
       [ 0.00450233]])

# 根据损失值停止,设定阈值为1E-6
runExpe(orig_data, theta, n, STOP_COST, thresh=0.000001, alpha=0.001)

***Original data - learning rate: 0.001 - Gradient descent - Stop: costs change < 1e-06
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