TensorFlow学习笔记(2):多元线性回归

https://segmentfault.com/a/1190000007969901

前言

本文使用tensorflow训练多元线性回归模型,并将其与scikit-learn做比较。数据集来自Andrew Ng的网上公开课程Deep Learning


In [4]:
import numpy as np
import tensorflow as tf

from sklearn import linear_model
from sklearn import preprocessing

x_data = np.loadtxt("input/ex3x.dat").astype(np.float32)
y_data = np.loadtxt("input/ex3y.dat").astype(np.float32)

reg = linear_model.LinearRegression()
reg.fit(x_data, y_data)
print("Coefficients of sklean: K=%s, b=%f" % (reg.coef_, reg.intercept_))

scaler = preprocessing.StandardScaler().fit(x_data)
print(scaler.mean_, scaler.scale_)

x_data_standard = scaler.transform(x_data)

W = tf.Variable(tf.zeros([2,1]))
b = tf.Variable(tf.zeros([1,1]))
y = tf.matmul(x_data_standard, W) + b

loss = tf.reduce_mean(tf.square(y - y_data.reshape(-1, 1))) / 2
optimizer = tf.train.GradientDescentOptimizer(0.3)
train = optimizer.minimize(loss)

init = tf.global_variables_initializer()

sess = tf.Session()
sess.run(init)

for step in range(100):
    sess.run(train)
    if step % 10 == 0:
        print(step, sess.run(W).flatten(), sess.run(b).flatten())
        
print("Coefficients of tensorflow(input should be standardized): K=%s, b=%s"
     % (sess.run(W).flatten(), sess.run(b).flatten()))
print("Coefficients of tensorflow(raw input): K=%s, b=%s"
      % (sess.run(W).flatten() / scaler.scale_, 
         sess.run(b).flatten() - np.dot(scaler.mean_ / scaler.scale_,
                                       sess.run(W))))


Coefficients of sklean: K=[  139.21072388 -8738.02148438], b=89597.805854
[ 2000.6809082      3.17021275] [  7.86202576e+02   7.52842903e-01]
0 [ 31729.23632812  16412.6484375 ] [ 102123.7890625]
10 [ 97174.78125      5595.25585938] [ 333681.59375]
20 [ 106480.5703125    -3611.31201172] [ 340222.53125]
30 [ 108727.5390625    -5858.10302734] [ 340407.28125]
40 [ 109272.953125     -6403.52148438] [ 340412.5]
50 [ 109405.3515625    -6535.91503906] [ 340412.625]
60 [ 109437.4921875    -6568.05371094] [ 340412.625]
70 [ 109445.296875     -6575.85644531] [ 340412.625]
80 [ 109447.1875       -6577.75097656] [ 340412.625]
90 [ 109447.640625     -6578.20654297] [ 340412.625]
Coefficients of tensorflow(input should be standardized): K=[ 109447.7421875    -6578.31152344], b=[ 340412.625]
Coefficients of tensorflow(raw input): K=[  139.21061707 -8737.9609375 ], b=[ 89597.78125]

思考

对于梯度下降算法,变量是否标准化很重要。在这个例子中,变量一个是面积,一个是房间数,量级相差很大,如果不归一化,面积在目标函数和梯度中就会占据主导地位,导致收敛极慢。