使用 Tensorflow 的多元线性回归模型
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【中文标题】使用 Tensorflow 的多元线性回归模型【英文标题】：Multiple Linear Regression Model by using Tensorflow 【发布时间】：2016-09-06 15:27:45 【问题描述】：我想使用 Tensorflow 构建一个多元线性回归模型。
数据集：Portland housing prices
一个数据例子：2104,3,399900（前两个是特征，最后一个是房价；我们有47个例子）
代码如下：
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
# model parameters as external flags
flags = tf.app.flags
FLAGS = flags.FLAGS
flags.DEFINE_float('learning_rate', 1.0, 'Initial learning rate.')
flags.DEFINE_integer('max_steps', 100, 'Number of steps to run trainer.')
flags.DEFINE_integer('display_step', 100, 'Display logs per step.')
def run_training(train_X, train_Y):
X = tf.placeholder(tf.float32, [m, n])
Y = tf.placeholder(tf.float32, [m, 1])
# weights
W = tf.Variable(tf.zeros([n, 1], dtype=np.float32), name="weight")
b = tf.Variable(tf.zeros([1], dtype=np.float32), name="bias")
# linear model
activation = tf.add(tf.matmul(X, W), b)
cost = tf.reduce_sum(tf.square(activation - Y)) / (2*m)
optimizer = tf.train.GradientDescentOptimizer(FLAGS.learning_rate).minimize(cost)
with tf.Session() as sess:
init = tf.initialize_all_variables()
sess.run(init)
for step in range(FLAGS.max_steps):
sess.run(optimizer, feed_dict=X: np.asarray(train_X), Y: np.asarray(train_Y))
if step % FLAGS.display_step == 0:
print "Step:", "%04d" % (step+1), "Cost=", ":.2f".format(sess.run(cost, \
feed_dict=X: np.asarray(train_X), Y: np.asarray(train_Y))), "W=", sess.run(W), "b=", sess.run(b)
print "Optimization Finished!"
training_cost = sess.run(cost, feed_dict=X: np.asarray(train_X), Y: np.asarray(train_Y))
print "Training Cost=", training_cost, "W=", sess.run(W), "b=", sess.run(b), '\n'
print "Predict.... (Predict a house with 1650 square feet and 3 bedrooms.)"
predict_X = np.array([1650, 3], dtype=np.float32).reshape((1, 2))
# Do not forget to normalize your features when you make this prediction
predict_X = predict_X / np.linalg.norm(predict_X)
predict_Y = tf.add(tf.matmul(predict_X, W),b)
print "House price(Y) =", sess.run(predict_Y)
def read_data(filename, read_from_file = True):
global m, n
if read_from_file:
with open(filename) as fd:
data_list = fd.read().splitlines()
m = len(data_list) # number of examples
n = 2 # number of features
train_X = np.zeros([m, n], dtype=np.float32)
train_Y = np.zeros([m, 1], dtype=np.float32)
for i in range(m):
datas = data_list[i].split(",")
for j in range(n):
train_X[i][j] = float(datas[j])
train_Y[i][0] = float(datas[-1])
else:
m = 47
n = 2
train_X = np.array( [[ 2.10400000e+03, 3.00000000e+00],
[ 1.60000000e+03, 3.00000000e+00],
[ 2.40000000e+03, 3.00000000e+00],
[ 1.41600000e+03, 2.00000000e+00],
[ 3.00000000e+03, 4.00000000e+00],
[ 1.98500000e+03, 4.00000000e+00],
[ 1.53400000e+03, 3.00000000e+00],
[ 1.42700000e+03, 3.00000000e+00],
[ 1.38000000e+03, 3.00000000e+00],
[ 1.49400000e+03, 3.00000000e+00],
[ 1.94000000e+03, 4.00000000e+00],
[ 2.00000000e+03, 3.00000000e+00],
[ 1.89000000e+03, 3.00000000e+00],
[ 4.47800000e+03, 5.00000000e+00],
[ 1.26800000e+03, 3.00000000e+00],
[ 2.30000000e+03, 4.00000000e+00],
[ 1.32000000e+03, 2.00000000e+00],
[ 1.23600000e+03, 3.00000000e+00],
[ 2.60900000e+03, 4.00000000e+00],
[ 3.03100000e+03, 4.00000000e+00],
[ 1.76700000e+03, 3.00000000e+00],
[ 1.88800000e+03, 2.00000000e+00],
[ 1.60400000e+03, 3.00000000e+00],
[ 1.96200000e+03, 4.00000000e+00],
[ 3.89000000e+03, 3.00000000e+00],
[ 1.10000000e+03, 3.00000000e+00],
[ 1.45800000e+03, 3.00000000e+00],
[ 2.52600000e+03, 3.00000000e+00],
[ 2.20000000e+03, 3.00000000e+00],
[ 2.63700000e+03, 3.00000000e+00],
[ 1.83900000e+03, 2.00000000e+00],
[ 1.00000000e+03, 1.00000000e+00],
[ 2.04000000e+03, 4.00000000e+00],
[ 3.13700000e+03, 3.00000000e+00],
[ 1.81100000e+03, 4.00000000e+00],
[ 1.43700000e+03, 3.00000000e+00],
[ 1.23900000e+03, 3.00000000e+00],
[ 2.13200000e+03, 4.00000000e+00],
[ 4.21500000e+03, 4.00000000e+00],
[ 2.16200000e+03, 4.00000000e+00],
[ 1.66400000e+03, 2.00000000e+00],
[ 2.23800000e+03, 3.00000000e+00],
[ 2.56700000e+03, 4.00000000e+00],
[ 1.20000000e+03, 3.00000000e+00],
[ 8.52000000e+02, 2.00000000e+00],
[ 1.85200000e+03, 4.00000000e+00],
[ 1.20300000e+03, 3.00000000e+00]]
).astype('float32')
train_Y = np.array([[ 399900.],
[ 329900.],
[ 369000.],
[ 232000.],
[ 539900.],
[ 299900.],
[ 314900.],
[ 198999.],
[ 212000.],
[ 242500.],
[ 239999.],
[ 347000.],
[ 329999.],
[ 699900.],
[ 259900.],
[ 449900.],
[ 299900.],
[ 199900.],
[ 499998.],
[ 599000.],
[ 252900.],
[ 255000.],
[ 242900.],
[ 259900.],
[ 573900.],
[ 249900.],
[ 464500.],
[ 469000.],
[ 475000.],
[ 299900.],
[ 349900.],
[ 169900.],
[ 314900.],
[ 579900.],
[ 285900.],
[ 249900.],
[ 229900.],
[ 345000.],
[ 549000.],
[ 287000.],
[ 368500.],
[ 329900.],
[ 314000.],
[ 299000.],
[ 179900.],
[ 299900.],
[ 239500.]]
).astype('float32')
return train_X, train_Y
def feature_normalize(train_X):
train_X_tmp = train_X.transpose()
for N in range(2):
train_X_tmp[N] = train_X_tmp[N] / np.linalg.norm(train_X_tmp[N])
train_X = train_X_tmp.transpose()
return train_X
import sys
def main(argv):
if not argv:
print "Enter data filename."
sys.exit()
filename = argv[1]
train_X, train_Y = read_data(filename, False)
train_X = feature_normalize(train_X)
run_training(train_X, train_Y)
if __name__ == '__main__':
tf.app.run()
我得到的结果：
使用 1.0 的学习率和 100 次迭代，该模型最终预测一栋 1650 平方英尺和 3 间卧室的房子的价格为 752,903 美元，其中：
培训成本= 4.94429e+09
W= [[ 505305.375] [ 177712.625]]
b= [247275.515625]
我的代码中一定有一些错误，因为不同学习率的成本函数图与solution不一样
按照解决方案的建议，我应该得到以下结果：
theta_0：340,413
theta_1：110,631
theta_2：-6,649
房子的预计价格应该是 293,081 美元。
我使用 tensorflow 有什么问题吗？
【问题讨论】：
为什么是张量流？这对您的情况来说太过分了（忽略许多其他错误，例如使用 GD 解决线性回归问题等） @user2717954 只是想熟悉一下 tensorflow.. 用梯度下降法解决这个问题不合适吗？ 线性回归有一个封闭形式的解决方案（最小二乘，wiki it up）。另外，如果您出于某种原因想使用 GD，我建议您从小得多的学习率开始（尝试 0.01，看看您的结果是否更好） 我通过减去平均值并除以标准差来修复特征归一化，学习率为 1.0 和 100 次迭代，我最终得到了与建议的解决方案相同的结果。谢谢！ 修改了下面的代码。 【参考方案1】：特征归一化应该通过减去均值并除以范围（或标准差）来完成。
def feature_normalize(train_X):
global mean, std
mean = np.mean(train_X, axis=0)
std = np.std(train_X, axis=0)
return (train_X - mean) / std
在进行此预测时不要忘记对特征进行归一化。
predict_X = (predict_X - mean)/std
【讨论】：
我想，你重新发明了***。 Sklearn 包含负责此类转换的对象scikit-learn.org/stable/modules/generated/…【参考方案2】：你应该试试：
for (x, y) in zip(train_X, train_Y):
sess.run(optimizer, feed_dict=X: x, Y: y)
代替：
sess.run(optimizer, feed_dict=X: np.asarray(train_X), Y: np.asarray(train_Y))
因为，您的代码只使用列表 train_X 和 train_Y 中的一个元素。
希望对你有帮助，
【讨论】：
【参考方案3】：试试这个
train_stats = train_X.describe()
train_stats = train_X.transpose()
def norm(x):
return (x - train_stats ['mean']) / train_stats ['std']
normed_train_data = norm(train_X)
【讨论】：
欢迎来到***。能否请您简要说明一下代码以及它如何解决问题中的问题？以上是关于使用 Tensorflow 的多元线性回归模型的主要内容，如果未能解决你的问题，请参考以下文章
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