求解逻辑回归—-梯度下降

scaled_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)

***Scaled data - learning rate: 0.001 - Gradient descent - Stop: 5000 iterations
Theta: [[ 0.32653044] [ 0.84802277] [ 0.78686591]] - Iter: 5000 - Last cost: 0.38 - Duration: 1.02s
array([[ 0.32653044],
       [ 0.84802277],
       [ 0.78686591]])

原始数据，只能达到达到0.61，而现在到达0.4以下，所以对数据做预处理是非常重要的

runExpe(scaled_data, theta, n, STOP_GRAD, thresh=0.02, alpha=0.001)

***Scaled data - learning rate: 0.001 - Gradient descent - Stop: gradient norm < 0.02
Theta: [[ 1.10868347] [ 2.57412148] [ 2.41283358]] - Iter: 58762 - Last cost: 0.22 - Duration: 12.75s
array([[ 1.10868347],
       [ 2.57412148],
       [ 2.41283358]])

更多的迭代次数会使得损失下降的更多

runExpe(scaled_data, theta, 16, STOP_GRAD, thresh=0.002*2, alpha=0.001)

***Scaled data - learning rate: 0.001 - Mini-batch (16) descent - Stop: gradient norm < 0.004
Theta: [[ 1.07757538] [ 2.51112557] [ 2.34671716]] - Iter: 54137 - Last cost: 0.22 - Duration: 5.31s
array([[ 1.07757538],
       [ 2.51112557],
       [ 2.34671716]])

#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))

accuracy = 60%
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