TensorFlow(九) 线性回归 (Linear Regression)

一. 线性回归是逻辑回归的基础，通俗来说，就是找到输出 X 与输入 Y 之间的关系。

二. 直接上代码，如下 :

# coding:utf-8

import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf

# Step 1: data construction
data = np.asarray([
    [6.2, 29.],
    [9.5, 44.],
    [10.5, 36.],
    [7.7, 37.],
    [8.6, 53.],
    [34.1, 68.],
    [11., 75.],
    [6.9, 18.],
    [7.3, 31.],
    [15.1, 25.],
    [29.1, 34.],
    [2.2, 14.],
    [5.7, 11.],
    [2., 11.],
    [2.5, 22.],
    [4., 16.],
    [5.4, 27.],
    [2.2, 9.],
    [7.2, 29.],
    [15.1, 30.],
    [16.5, 40.],
    [18.4, 32.],
    [36.2, 41.],
    [39.7, 147.],
    [18.5, 22.],
    [23.3, 29.],
    [12.2, 46.],
    [5.6, 23.],
    [21.8, 4.],
    [21.6, 31.],
    [9., 39.],
    [3.6, 15.],
    [5., 32.],
    [28.6, 27.],
    [17.4, 32.],
    [11.3, 34.],
    [3.4, 17.],
    [11.9, 46.],
    [10.5, 42.],
    [10.7, 43.],
    [10.8, 34.],
    [4.8, 19.]])
n_samples = data.shape[0]

# Step 2: create placeholders for input X and label Y
X = tf.placeholder(tf.float32, name='X')
Y = tf.placeholder(tf.float32, name='Y')

# Step 3: create weight and bias, initialized to 0
w = tf.Variable(0.0, name='weights')
b = tf.Variable(0.0, name='bias')

# Step 4: build model to predict Y
Y_predicted = X * w + b

# Step 5: use the square error as the loss function
loss = tf.square(Y - Y_predicted, name='loss')

# Step 6: using gradient descent with learning rate of 0.001 to minimize loss
optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.001).minimize(loss)

# Step 7: train the model for 50 epochs
with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    for i in range(50):
        total_loss = 0
        for x, y in data:
            # Session runs train_op and fetch values of loss
            _, sub_loss = sess.run([optimizer, loss], feed_dict={X: x, Y: y})
            total_loss += sub_loss
        print('Epoch {0}: {1}'.format(i, total_loss/n_samples))

    # Step 8: output the values of w and b
    w, b = sess.run([w, b])
    print("w:[", w, "] b[", b, "]")

# Step 9: draw the result
X, Y = data.T[0], data.T[1]
plt.plot(X, Y, 'bo', label='Real data')
plt.plot(X, X * w + b, 'r', label='Predicted data')
plt.legend()
plt.show()

代码中的 data 是 ( X, Y ) 数据序列对。

三. 输出

Console 输出为

Epoch 0: 2069.6319333978354
Epoch 1: 2117.0123581953535
Epoch 2: 2092.302723001866
Epoch 3: 2068.5080461938464
Epoch 4: 2045.591184088162
Epoch 5: 2023.5146448101316
Epoch 6: 2002.2447619835536
Epoch 7: 1981.748338803649
Epoch 8: 1961.9944411260742
Epoch 9: 1942.9520116143283
Epoch 10: 1924.5930823644712
Epoch 11: 1906.8898800636332
Epoch 12: 1889.8164505837929
Epoch 13: 1873.347133841543
Epoch 14: 1857.4588400604468
Epoch 15: 1842.1278742424079
Epoch 16: 1827.332495119955
Epoch 17: 1813.0520579712022
Epoch 18: 1799.2660847636982
Epoch 19: 1785.9562132299961
Epoch 20: 1773.1024853109072
Epoch 21: 1760.689129482884
Epoch 22: 1748.6984157081515
Epoch 23: 1737.1138680398553
Epoch 24: 1725.920873066732
Epoch 25: 1715.1046249579008
Epoch 26: 1704.6500954309377
Epoch 27: 1694.5447134910141
Epoch 28: 1684.7746311347667
Epoch 29: 1675.328450968245
Epoch 30: 1666.1935385839038
Epoch 31: 1657.3584002084322
Epoch 32: 1648.8122658529207
Epoch 33: 1640.5440742547091
Epoch 34: 1632.5446836102221
Epoch 35: 1624.8043315147183
Epoch 36: 1617.3126799958602
Epoch 37: 1610.0622532456405
Epoch 38: 1603.0433557207386
Epoch 39: 1596.2479176106197
Epoch 40: 1589.668056331575
Epoch 41: 1583.2965242617897
Epoch 42: 1577.126371285745
Epoch 43: 1571.1501190634
Epoch 44: 1565.360979151513
Epoch 45: 1559.7523780798629
Epoch 46: 1554.3184364555138
Epoch 47: 1549.0529469620615
Epoch 48: 1543.950059985476
Epoch 49: 1539.0050282141283
w:[ 1.99747 ] b[ 12.5687 ]

绘制输出为

我们预测的直线模型就是图中的红色直线，该直线模拟了空间里点的分布方向。

如果要更精确地对空间里点的分布进行模拟，则需要适当复杂的模型以及随之更多的参数。

TensorFlow(九) 线性回归 (Linear Regression)

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