TensorFlow訓練單特征和多特征的線性回歸

線性回歸

線性回歸是很常見的一種回歸，線性回歸可以用來預測或者分類，主要解決線性問題。相關知識可看“相關閱讀”。

主要思想

在TensorFlow中進行線性回歸處理重點是將樣本和樣本特征矩陣化。

單特征線性回歸

單特征回歸模型為：y=wx+b

構建模型

X = tf.placeholder(tf.float32, [None, 1])
w = tf.Variable(tf.zeros([1, 1]))
b = tf.Variable(tf.zeros([1]))
y = tf.matmul(X, w) + b
Y = tf.placeholder(tf.float32, [None, 1])

構建成本函數

cost = tf.reduce_mean(tf.square(Y-y))

梯度下降最小化成本函數，梯度下降步長為0.01

train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cost)

完整代碼，迭代次數為10000

import tensorflow as tfX = tf.placeholder(tf.float32, [None, 1])
w = tf.Variable(tf.zeros([1, 1]))
b = tf.Variable(tf.zeros([1]))
y = tf.matmul(X, w) + b
Y = tf.placeholder(tf.float32, [None, 1])# 成本函數 sum(sqr(y_-y))/n
cost = tf.reduce_mean(tf.square(Y-y))# 用梯度下降訓練
train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cost)init = tf.initialize_all_variables()
sess = tf.Session()
sess.run(init)x_train = [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
y_train = [[10],[11.5],[12],[13],[14.5],[15.5],[16.8],[17.3],[18],[18.7]]for i in range(10000):sess.run(train_step, feed_dict={X: x_train, Y: y_train})
print("w:%f" % sess.run(w))
print("b:%f" % sess.run(b))

多特征線性回歸

多特征回歸模型為：y=(w1x1+w2x2+...+wnxn)+b，寫為y=wx+b。

y為m行1列矩陣，x為m行n列矩陣，w為n行1列矩陣。TensorFlow中用如下來表示模型。

構建模型

X = tf.placeholder(tf.float32, [None, n])
w = tf.Variable(tf.zeros([n, 1]))
b = tf.Variable(tf.zeros([1]))
y = tf.matmul(X, w) + b
Y = tf.placeholder(tf.float32, [None, 1])

構建成本函數

cost = tf.reduce_mean(tf.square(Y-y))

梯度下降最小化成本函數，梯度下降步長為0.01

train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cost)

完整代碼，迭代次數為10000

import tensorflow as tfX = tf.placeholder(tf.float32, [None, 2])
w = tf.Variable(tf.zeros([2, 1]))
b = tf.Variable(tf.zeros([1]))
y = tf.matmul(X, w) + b
Y = tf.placeholder(tf.float32, [None, 1])# 成本函數 sum(sqr(y_-y))/n
cost = tf.reduce_mean(tf.square(Y-y))# 用梯度下降訓練
train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cost)init = tf.initialize_all_variables()
sess = tf.Session()
sess.run(init)x_train = [[1, 2], [2, 1], [2, 3], [3, 5], [1, 3], [4, 2], [7, 3], [4, 5], [11, 3], [8, 7]]
y_train = [[7], [8], [10], [14], [8], [13], [20], [16], [28], [26]]for i in range(10000):sess.run(train_step, feed_dict={X: x_train, Y: y_train})
print("w0:%f" % sess.run(w[0]))
print("w1:%f" % sess.run(w[1]))
print("b:%f" % sess.run(b))