多项式回归给使用Tensorflow

Question

错误的答案我已经有了一套玩具数据的格式如下：

x - x**2 + x**3 

我试图创建一个使用Tensorflow预测的权重，Python脚本在哪这种情况应该是[1，-1，1]。但是，当我运行它时，我提出了荒谬的答案。

这是我的代码：

# Optional; supresses warnings about GPU 
import os 
os.environ['TF_CPP_MIN_LOG_LEVEL']='2' 

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

# Read the data 
COLUMNS = ["url", "title_length", "article_length", "keywords", "shares"] 
data = np.genfromtxt("OnlineNewsPopularityNonLinear.csv", delimiter=',', names=COLUMNS) 

# Determine how many data points we're using and the order of the equation 
number_of_records = data.size 
equation_order = 3 

# Set up the variables for weights and bias, but as matrices 
w = tf.Variable(np.zeros([equation_order, 1]), dtype="float32", name="w") 
b = tf.Variable(np.zeros([1]), dtype="float32", name="b") 

content_info_temp = np.zeros([number_of_records, equation_order]) 
content_info = tf.placeholder("float32", shape=[number_of_records, equation_order]) 
actual_shares = tf.placeholder("float32") 

# Input data should be a matrix of [number_of_records, equation_order] where 
# each value has been raised to the appropriate power, according to 
# our model. We'll need to call it 
for i in range(equation_order): 
    print (i) 
    content_info_temp[:, i] = np.power(data["article_length"], (i+1))/np.max(np.power(data["article_length"], (i+1))) 

# Create the prediction; it's still y = mx + b, but in this case 
# m is a matrix of weights, and x is a matrix of values 
predicted_shares = tf.add(tf.matmul(content_info, w), b) 

# Loss is the same as before. 
error = tf.reduce_mean(tf.square(predicted_shares - actual_shares)) 

# Create the optimizer 
step_size = .001 
optimizer = tf.train.GradientDescentOptimizer(step_size).minimize(error) 

# Create the model 
model = tf.global_variables_initializer() 

# Create the session to run the algorith 
with tf.Session() as session: 

    # Initialize everything 
    session.run(model) 

    # Run the algorithm 
    for i in range(100000): 
     #Just as before, we run the algorithm, but we're feeding in normalized matrixes rather than single values 
     #session.run(optimizer, feed_dict={content_info: input_data, actual_shares: data['shares']/np.max(data["shares"])}) 
     session.run(optimizer, feed_dict={content_info: content_info_temp, actual_shares: data['shares']/np.max(data['shares'])}) 
     # Display every 100 results 
     if (i % 100 == 0): 
     print (session.run(w)) 
     #print (session.run(predicted_shares - actual_shares)) 

    #Display the final result  
    w_value = session.run(w) 

    print ("FINAL:") 
    print (w_value) 

    print (w_value[0]*np.max(data["article_length"])) 
    print (w_value[1]*np.max(session.run(tf.pow(data["article_length"], 2)))) 
    print (w_value[2]*np.max(session.run(tf.pow(data["article_length"], 3)))) 

如果我跑，我得到：

去正火前：

[[ 0.14678337] 
[ 0.01708614] 
[-0.01448759]] 

去正火后：

[ 141.49916077] 
[ 15878.08398438] 
[-12978583.] 

万一它很重要（我认为它不）我使用Tensorflow 1.2。

任何想法？谢谢...

[主要编辑：

OK，根据意见，我已经修改了代码，如下所示：

import numpy as np 
import tensorflow as tf 

# Read the data 
COLUMNS = ["url", "title_length", "article_length", "keywords", "shares", "shares2"] 
data = np.genfromtxt("OnlineNewsPopularityNonLinear.csv", delimiter=',', names=COLUMNS) 

x_raw = data["article_length"] 

x_data = np.zeros([3, 100]) 
x_data[0] = x_raw/np.max(x_raw) 
x_data[1] = x_raw**2/np.max(x_raw**2) 
x_data[2] = x_raw**3/np.max(x_raw**3) 

print(x_data) 

w_set = np.zeros([1, 3]) 
w_set[0] = np.array([1, -1, 1]) 

print(w_set) 

#y_data = np.matmul(w_set, x_data) 
y_data = np.zeros([1, 100]) 
y_data[0] = data["shares"]/np.max(data["shares"]) 

print(y_data) 

w = tf.Variable(np.zeros([1, 3]), dtype="float32", name="w") 
b = tf.Variable(np.zeros([1]), dtype="float32", name="b") 

X = tf.placeholder("float32", shape=[3, 100]) 
Y = tf.placeholder("float32", shape=[1, 100]) 

Ypred = tf.add(tf.matmul(w, X), b) 

error = tf.reduce_mean(tf.squared_difference(Ypred, Y)) 
optimizer = tf.train.GradientDescentOptimizer(.01).minimize(error) 


init = tf.global_variables_initializer() 

# Create the session to run the algorith 
with tf.Session() as session: 
    session.run(init) 

    # Run the algorithm 
    for i in range(5000000): 
     _, loss, Wcur = session.run([optimizer, error, w], feed_dict={X: x_data, Y: y_data}) 
     if (i % 10000 == 0): 
      print (loss, Wcur) 

当我人为地使数据按照适当的权重（1，-1，1），它工作正常。当我用“真实”的数据（你可以在这里找到：http://www.nicholaschase.com/OnlineNewsPopularityNonLinear.csv）似乎与

2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 
2.67402e-10 [[-0.00169705 0.00216109 0.99922621]] 

来拉平“真实”数据与电子表格创建的，所以它应该只是准确的，不是吗？

谢谢...]

Answer 1

首先：你的意思是

x[0] - x[1]**2 + x[2]**3 

下，很难不将数据运行代码。我会从理智检查开始，测试你的数据是否真的遵循给定的等式。我猜想事实并非如此。因为一个真正的MWE是正确的

import numpy as np 
import tensorflow as tf 

number_of_records = 1000 
equation_order = 3 

# toy data 
X_data = np.random.randn(number_of_records, equation_order) 
X_data[1] = X_data[1]**2 
X_data[2] = X_data[2]**3 
Y_data = np.matmul(X_data, np.array([[1], [-1], [1.]])) 

w = tf.Variable(np.zeros([equation_order, 1]), dtype="float32", name="w") 
b = tf.Variable(np.zeros([1]), dtype="float32", name="b") 

X = tf.placeholder("float32", shape=[None, equation_order]) 
Y = tf.placeholder("float32", shape=[None, 1]) 

Ypred = tf.add(tf.matmul(X, w), b) 

error = tf.reduce_mean(tf.squared_difference(Ypred, Y)) 
optimizer = tf.train.GradientDescentOptimizer(.1).minimize(error) 


init = tf.global_variables_initializer() 

# Create the session to run the algorith 
with tf.Session() as session: 
    session.run(init) 

    # Run the algorithm 
    for _ in range(200): 
     _, loss, Wcur = session.run([optimizer, error, w], feed_dict={X: X_data, Y: Y_data}) 
     print loss, Wcur.transpose() 

，并返回

5.33256e-14 [[ 0.99999988 -0.99999988 0.99999988]] 

我会说这看起来很可疑：如果您打印错误的梯度下降循环的每个迭代

for i in range(equation_order): 
    print (i) 
    content_info_temp[:, i] = np.power(data["article_length"], (i+1))/np.max(np.power(data["article_length"], (i+1)))