0.完整代码
下面一段代码实现了2个功能： 1.用keras库编程实现拟合线性方程的回归模型； 2.对比了4种优化器的性能。
代码语言：javascript复制from keras.models import Sequential
from keras.layers import Dense
import numpy as np
from keras import optimizers
if __name__ == '__main__':
w = 2.5
b = 1.5
X = np.linspace(2, 100, 50)
Y = X * w b
print('X[:5]:', X[:5])
print('Y[:5]:', Y[:5])
adam = optimizers.Adam(lr=0.02)
sgd = optimizers.SGD(lr=0.0002)
adagrad = optimizers.Adagrad(lr=0.3)
adadelta = optimizers.Adadelta(lr=0.3)
optimizer_list = [adam, sgd, adagrad, adadelta]
epochs_list = [100, 200, 500, 1000]
for epochs in epochs_list:
for optimizer in optimizer_list:
model = Sequential()
model.add(Dense(input_dim=1, units=1))
model.compile(loss='mse', optimizer=optimizer)
model.fit(X, Y, steps_per_epoch=10, epochs=epochs, verbose=False)
trained_w = model.layers[0].get_weights()[0][0][0]
trained_b = model.layers[0].get_weights()[1][0]
w_error = abs(trained_w - w)
b_error = abs(trained_b - b)
print('epochs:%d, 优化器种类:%s,t w误差:%.4f, b误差:%.4f'
%(epochs, optimizer.__class__, w_error, b_error))上面一段代码的运行结果如下：
代码语言：javascript复制 X[:5]: [ 2. 4. 6. 8. 10.]
Y[:5]: [ 6.5 11.5 16.5 21.5 26.5]
epochs:100, 优化器种类:<class 'keras.optimizers.Adam'>, w误差:0.0083, b误差:0.5539
epochs:100, 优化器种类:<class 'keras.optimizers.SGD'>, w误差:0.0195, b误差:1.3155
epochs:100, 优化器种类:<class 'keras.optimizers.Adagrad'>, w误差:0.0297, b误差:1.9919
epochs:100, 优化器种类:<class 'keras.optimizers.Adadelta'>, w误差:0.4450, b误差:0.9875
epochs:200, 优化器种类:<class 'keras.optimizers.Adam'>, w误差:0.0032, b误差:0.2133
epochs:200, 优化器种类:<class 'keras.optimizers.SGD'>, w误差:0.0181, b误差:1.2160
epochs:200, 优化器种类:<class 'keras.optimizers.Adagrad'>, w误差:0.0046, b误差:0.3051
epochs:200, 优化器种类:<class 'keras.optimizers.Adadelta'>, w误差:0.3739, b误差:0.3786
epochs:500, 优化器种类:<class 'keras.optimizers.Adam'>, w误差:0.0000, b误差:0.0000
epochs:500, 优化器种类:<class 'keras.optimizers.SGD'>, w误差:0.0135, b误差:0.9093
epochs:500, 优化器种类:<class 'keras.optimizers.Adagrad'>, w误差:0.0050, b误差:0.3327
epochs:500, 优化器种类:<class 'keras.optimizers.Adadelta'>, w误差:0.0027, b误差:0.0172
epochs:1000, 优化器种类:<class 'keras.optimizers.Adam'>, w误差:0.0000, b误差:0.0000
epochs:1000, 优化器种类:<class 'keras.optimizers.SGD'>, w误差:0.0083, b误差:0.5563
epochs:1000, 优化器种类:<class 'keras.optimizers.Adagrad'>, w误差:0.0141, b误差:0.9425
epochs:1000, 优化器种类:<class 'keras.optimizers.Adadelta'>, w误差:0.0101, b误差:0.4870
从上面的运行结果可以看出： 在epochs为100时，Adam优化器效果最优，SGD优化器次优； 在epochs为200时，Adam优化器效果最优，Adagrad优化器次优； 在epochs为500时，Adam优化器效果最优，Adadelta优化器次优； 在epochs为1000时，Adam优化器效果最优。
1.结论
对于线性方程的回归模型，使用Adam优化器能够得到不错的拟合效果。
