我试图理解线性回归……这是我试图理解的脚本:

'''
A linear regression learning algorithm example using TensorFlow library.
Author: Aymeric Damien
Project: https://github.com/aymericdamien/TensorFlow-Examples/
'''

from __future__ import print_function

import tensorflow as tf
from numpy import *
import numpy
import matplotlib.pyplot as plt
rng = numpy.random

# Parameters
learning_rate = 0.0001
training_epochs = 1000
display_step = 50

# Training Data
train_X = numpy.asarray([3.3,4.4,5.5,6.71,6.93,4.168,9.779,6.182,7.59,2.167,
                         7.042,10.791,5.313,7.997,5.654,9.27,3.1])
train_Y = numpy.asarray([1.7,2.76,2.09,3.19,1.694,1.573,3.366,2.596,2.53,1.221,
                         2.827,3.465,1.65,2.904,2.42,2.94,1.3])

train_X=numpy.asarray(train_X)
train_Y=numpy.asarray(train_Y)
n_samples = train_X.shape[0]


# tf Graph Input
X = tf.placeholder("float")
Y = tf.placeholder("float")

# Set model weights
W = tf.Variable(rng.randn(), name="weight")
b = tf.Variable(rng.randn(), name="bias")

# Construct a linear model
pred = tf.add(tf.multiply(X, W), b)


# Mean squared error
cost = tf.reduce_sum(tf.pow(pred-Y, 2))/(2*n_samples)
# Gradient descent
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

# Initializing the variables
init = tf.global_variables_initializer()

# Launch the graph
with tf.Session() as sess:
    sess.run(init)

    # Fit all training data
    for epoch in range(training_epochs):
        for (x, y) in zip(train_X, train_Y):
            sess.run(optimizer, feed_dict={X: x, Y: y})

        # Display logs per epoch step
        if (epoch+1) % display_step == 0:
            c = sess.run(cost, feed_dict={X: train_X, Y:train_Y})
            print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(c), \
                "W=", sess.run(W), "b=", sess.run(b))

    print("Optimization Finished!")
    training_cost = sess.run(cost, feed_dict={X: train_X, Y: train_Y})
    print("Training cost=", training_cost, "W=", sess.run(W), "b=", sess.run(b), '\n')

    # Graphic display
    plt.plot(train_X, train_Y, 'ro', label='Original data')
    plt.plot(train_X, sess.run(W) * train_X + sess.run(b), label='Fitted line')
    plt.legend()
    plt.show()

# Set model weights
W = tf.Variable(rng.randn(), name="weight")
b = tf.Variable(rng.randn(), name="bias")

最佳答案

让我们试着把一些直觉和来源与 tf 放在一起方法。

一般直觉:

这里介绍的回归是一个监督学习问题。其中，如 Russel&Norvig 的 Artificial Intelligence 中所定义，任务是:

given a training set (X, y) of m input-output pairs (x1, y1), (x2, y2), ... , (xm, ym), where each output was generated by an unknown function y = f(x), discover a function h that approximates the true function f

from __future__ import absolute_import, division, print_function
import numpy as np
import tensorflow as tf

####################################################################################################
### GLOBALS
####################################################################################################
DIMENSIONS = 5
f = lambda(x): sum(x) # the "true" function: f = 0 + 1*x1 + 1*x2 + 1*x3 ...
noise = lambda: np.random.normal(0,10) # some noise

####################################################################################################
### GRADIENT DESCENT APPROACH
####################################################################################################
# dataset globals
DS_SIZE = 5000
TRAIN_RATIO = 0.6 # 60% of the dataset is used for training
_train_size = int(DS_SIZE*TRAIN_RATIO)
_test_size = DS_SIZE - _train_size
ALPHA = 1e-8 # learning rate
LAMBDA = 0.5 # L2 regularization factor
TRAINING_STEPS = 1000

# generate the dataset, the labels and split into train/test
ds = [[np.random.rand()*1000 for d in range(DIMENSIONS)] for _ in range(DS_SIZE)] # synthesize data
# ds = normalize_data(ds)
ds = [(x, [f(x)+noise()]) for x in ds] # add labels
np.random.shuffle(ds)
train_data, train_labels = zip(*ds[0:_train_size])
test_data, test_labels = zip(*ds[_train_size:])

# define the computational graph
graph = tf.Graph()
with graph.as_default():
  # declare graph inputs
  x_train = tf.placeholder(tf.float32, shape=(_train_size, DIMENSIONS))
  y_train = tf.placeholder(tf.float32, shape=(_train_size, 1))
  x_test = tf.placeholder(tf.float32, shape=(_test_size, DIMENSIONS))
  y_test = tf.placeholder(tf.float32, shape=(_test_size, 1))
  theta = tf.Variable([[0.0] for _ in range(DIMENSIONS)])
  theta_0 = tf.Variable([[0.0]]) # don't forget the bias term!
  # forward propagation
  train_prediction = tf.matmul(x_train, theta)+theta_0
  test_prediction  = tf.matmul(x_test, theta) +theta_0
  # cost function and optimizer
  train_cost = (tf.nn.l2_loss(train_prediction - y_train)+LAMBDA*tf.nn.l2_loss(theta))/float(_train_size)
  optimizer = tf.train.GradientDescentOptimizer(ALPHA).minimize(train_cost)
  # test results
  test_cost = (tf.nn.l2_loss(test_prediction - y_test)+LAMBDA*tf.nn.l2_loss(theta))/float(_test_size)

# run the computation
with tf.Session(graph=graph) as s:
  tf.initialize_all_variables().run()
  print("initialized"); print(theta.eval())
  for step in range(TRAINING_STEPS):
    _, train_c, test_c = s.run([optimizer, train_cost, test_cost],
                               feed_dict={x_train: train_data, y_train: train_labels,
                                          x_test: test_data, y_test: test_labels })
    if (step%100==0):
      # it should return bias close to zero and parameters all close to 1 (see definition of f)
      print("\nAfter", step, "iterations:")
      #print("   Bias =", theta_0.eval(), ", Weights = ", theta.eval())
      print("   train cost =", train_c); print("   test cost =", test_c)
  PARAMETERS_GRADDESC = tf.concat(0, [theta_0, theta]).eval()
  print("Solution for parameters:\n", PARAMETERS_GRADDESC)

####################################################################################################
### NORMAL EQUATIONS APPROACH
####################################################################################################
# dataset globals
DIMENSIONS = 5
DS_SIZE = 5000
TRAIN_RATIO = 0.6 # 60% of the dataset isused for training
_train_size = int(DS_SIZE*TRAIN_RATIO)
_test_size = DS_SIZE - _train_size
f = lambda(x): sum(x) # the "true" function: f = 0 + 1*x1 + 1*x2 + 1*x3 ...
noise = lambda: np.random.normal(0,10) # some noise
# training globals
LAMBDA = 1e6 # L2 regularization factor

# generate the dataset, the labels and split into train/test
ds = [[np.random.rand()*1000 for d in range(DIMENSIONS)] for _ in range(DS_SIZE)]
ds = [([1]+x, [f(x)+noise()]) for x in ds] # add x[0]=1 dimension and labels
np.random.shuffle(ds)
train_data, train_labels = zip(*ds[0:_train_size])
test_data, test_labels = zip(*ds[_train_size:])

# define the computational graph
graph = tf.Graph()
with graph.as_default():
  # declare graph inputs
  x_train = tf.placeholder(tf.float32, shape=(_train_size, DIMENSIONS+1))
  y_train = tf.placeholder(tf.float32, shape=(_train_size, 1))
  theta = tf.Variable([[0.0] for _ in range(DIMENSIONS+1)]) # implicit bias!
  # optimum
  optimum = tf.matrix_solve_ls(x_train, y_train, LAMBDA, fast=True)

# run the computation: no loop needed!
with tf.Session(graph=graph) as s:
  tf.initialize_all_variables().run()
  print("initialized")
  opt = s.run(optimum, feed_dict={x_train:train_data, y_train:train_labels})
  PARAMETERS_NORMEQ = opt
  print("Solution for parameters:\n",PARAMETERS_NORMEQ)

####################################################################################################
### PREDICTION AND ERROR RATE
####################################################################################################

# generate test dataset
ds = [[np.random.rand()*1000 for d in range(DIMENSIONS)] for _ in range(DS_SIZE)]
ds = [([1]+x, [f(x)+noise()]) for x in ds] # add x[0]=1 dimension and labels
test_data, test_labels = zip(*ds)
# define hypothesis
h_gd = lambda(x): PARAMETERS_GRADDESC.T.dot(x)
h_ne = lambda(x): PARAMETERS_NORMEQ.T.dot(x)
# define cost
mse = lambda pred, lab: ((pred-np.array(lab))**2).sum()/DS_SIZE
# make predictions!
predictions_gd = np.array([h_gd(x) for x in test_data])
predictions_ne = np.array([h_ne(x) for x in test_data])
# calculate and print total error
cost_gd = mse(predictions_gd, test_labels)
cost_ne = mse(predictions_ne, test_labels)
print("total cost with gradient descent:", cost_gd)
print("total cost with normal equations:", cost_ne)

关于python - 使用 tensorflow 进行线性回归，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/43170017/