计算线性回归问题中的权重 [英] Computing weights in linear regression problem

问题描述

我已经编写了演示线性回归算法的脚本，如下所示:

I have written the script that demonstrates the linear regression algorithm as follows:

training_epochs = 100
learning_rate = 0.01
# the training set
x_train = np.linspace(0, 10, 100)
y_train = x_train + np.random.normal(0,1,100)
# set up placeholders for input and output
X = tf.placeholder(tf.float32)
Y = tf.placeholder(tf.float32)
# set up variables for weights
w0 = tf.Variable(0.0, name="w0")
w1 = tf.Variable(0.0, name="w1")
y_predicted =  X*w1 + w0
# Define the cost function
costF = 0.5*tf.square(Y-y_predicted)
# Define the operation that will be called on each iteration
train_op = tf.train.GradientDescentOptimizer(learning_rate).minimize(costF)
sess = tf.Session()
init = tf.global_variables_initializer()
sess.run(init)
# Loop through the data training
for epoch in range(training_epochs):
       for (x, y) in zip(x_train, y_train):
              sess.run(train_op, feed_dict={X: x, Y: y})
# get values of the final weights
w_val_0,w_val_1 = sess.run([w0,w1])
sess.close()

使用上面的脚本，我可以轻松地计算w_val_1和w_val_0.但是，如果我使用y_predicted进行了一些更改:

With this script above, I could compute w_val_1 and w_val_0 easily. But if I changed something with the y_predicted:

w0 = tf.Variable(0.0, name="w0")
w1 = tf.Variable(0.0, name="w1")
w2 = tf.Variable(0.0, name="w2")
y_predicted =  X*X*w2 + X*w1 + w0
...
w_val_0,w_val_1,w_val_2 = sess.run([w0,w1,w2])

然后我无法计算w_val_0，w_val_1，w_val_2.请帮帮我！

then I couldn't compute w_val_0, w_val_1, w_val_2. Please help me!

推荐答案

当您进行 X * X 重量( w2 ， w1 和 w0 )迅速增加，达到 inf ，这会导致 nan 值的损失，并且不会进行训练.根据经验，总是将数据标准化为0均值和单位方差.

When you are doing X*X the weight (w2, w1 and w0) increase rapidly reaching inf which results in nan values in the loss and no training happens. As a rule of thumb always normalize the data to 0 mean and unit variance.

training_epochs = 100
learning_rate = 0.01
# the training set
x_train = np.linspace(0, 10, 100)
y_train = x_train + np.random.normal(0,1,100)
                                     
# # Normalize the data
x_mean = np.mean(x_train)
x_std = np.std(x_train)
x_train_ = (x_train - x_mean)/x_std

X = tf.placeholder(tf.float32)
Y = tf.placeholder(tf.float32)
# set up variables for weights
w0 = tf.Variable(0.0, name="w0")
w1 = tf.Variable(0.0, name="w1")
w2 = tf.Variable(0.0, name="w3")

y_predicted =  X*X*w1 + X*w2 + w0
# Define the cost function
costF = 0.5*tf.square(Y-y_predicted)
# Define the operation that will be called on each iteration
train_op = tf.train.GradientDescentOptimizer(learning_rate).minimize(costF)
sess = tf.Session()
init = tf.global_variables_initializer()
sess.run(init)
# Loop through the data training
for epoch in range(training_epochs):
       for (x, y) in zip(x_train_, y_train):
            sess.run(train_op, feed_dict={X: x, Y: y})                                


y_hat = sess.run(y_predicted, feed_dict={X: x_train_})
print (sess.run([w0,w1,w2]))
sess.close()

plt.plot(x_train, y_train)
plt.plot(x_train, y_hat)
plt.show()

输出:

[4.9228806, -0.08735728, 3.029659]

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