python - tensorflow 的线性回归得到明显的均方误差

Question

我是 tensorflow 的新手，我正在尝试为回归实现一个简单的前馈网络，仅用于学习目的。完整的可执行代码如下。

回归均方误差在 6 左右，相当大。有点出乎意料，因为回归函数是线性且简单的 2*x+y，我期待更好的性能。

I am asking for help to check if I did anything wrong in the code. I carefully checked the matrix dimensions so that should be good, but it is possible that I misunderstand something so the network or the session is not properly configured (like, should I run the training session multiple times, instead of just one time (the code below enclosed by #TRAINING#)? I see in some examples they input data piece by piece, and run the training progressively. I run the training just one time and input all data).

如果代码不错，也许这是一个建模问题，但我真的不希望使用复杂的网络进行如此简单的回归。

import tensorflow as tf
import numpy as np
from sklearn.metrics import mean_squared_error

# inputs are points from a 100x100 grid in domain [-2,2]x[-2,2], total 10000 points
lsp = np.linspace(-2,2,100)
gridx,gridy = np.meshgrid(lsp,lsp)
inputs = np.dstack((gridx,gridy))
inputs = inputs.reshape(-1,inputs.shape[-1]) # reshpaes the grid into a 10000x2 matrix
feature_size = inputs.shape[1] # feature_size is 2, features are the 2D coordinates of each point
input_size = inputs.shape[0] # input_size is 10000

# a simple function f(x)=2*x[0]+x[1] to regress
f = lambda x: 2 * x[0] + x[1]
label_size = 1
labels = f(inputs.transpose()).reshape(-1,1) # reshapes labels as a column vector

ph_inputs = tf.placeholder(tf.float32, shape=(None, feature_size), name='inputs')
ph_labels = tf.placeholder(tf.float32, shape=(None, label_size), name='labels')

# just one hidden layer with 16 units
hid1_size = 16
w1 = tf.Variable(tf.random_normal([hid1_size, feature_size], stddev=0.01), name='w1')
b1 = tf.Variable(tf.random_normal([hid1_size, label_size]), name='b1')
y1 = tf.nn.relu(tf.add(tf.matmul(w1, tf.transpose(ph_inputs)), b1))

# the output layer
wo = tf.Variable(tf.random_normal([label_size, hid1_size], stddev=0.01), name='wo')
bo = tf.Variable(tf.random_normal([label_size, label_size]), name='bo')
yo = tf.transpose(tf.add(tf.matmul(wo, y1), bo))

# defines optimizer and predictor
lr = tf.placeholder(tf.float32, shape=(), name='learning_rate')
loss = tf.losses.mean_squared_error(ph_labels,yo)
optimizer = tf.train.GradientDescentOptimizer(lr).minimize(loss)
predictor = tf.identity(yo)

# TRAINING 
init = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init)
_, c = sess.run([optimizer, loss], feed_dict={lr:0.05, ph_inputs: inputs, ph_labels: labels})
# TRAINING 

# gets the regression results
predictions = np.zeros((input_size,1))
for i in range(input_size):
    predictions[i] = sess.run(predictor, feed_dict={ph_inputs: inputs[i, None]}).squeeze()

# prints regression MSE
print(mean_squared_error(predictions, labels))

Answer 1

你是对的，你自己理解了问题。

事实上，问题在于您只运行了一次优化步骤。因此，您只需执行一个网络参数更新步骤，因此成本不会降低。

我刚刚更改了您代码的训练 session ，以使其按预期工作(100 个训练步骤):

# TRAINING
init = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init)
for i in range(100):
    _, c = sess.run(
        [optimizer, loss],
        feed_dict={
            lr: 0.05,
            ph_inputs: inputs,
            ph_labels: labels
        })
    print("Train step {} loss value {}".format(i, c))
# TRAINING

在训练步骤结束时，我去:

Train step 99 loss value 0.04462708160281181

0.044106700712455045