In [3]:
"""
Linear Regression with TensorFlow
parksurk@gmail.com
"""
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
#matplotlib inline
print ("Packages are loaded!!!")
In [6]:
# Generate training data
np.random.seed(1)
def f(x, a, b):
n = train_X.size
vals = np.zeros((1, n))
for i in range(0, n):
ax = np.multiply(a, x.item(i))
val = np.add(ax, b)
vals[0, i] = val
return vals
Wref = 0.7
bref = -1.
n = 20
noise_var = 0.001
train_X = np.random.random((1,n))
ref_Y = f(train_X, Wref, bref)
train_Y = ref_Y + np.sqrt(noise_var)*np.random.randn(1,n)
n_samples = train_X.size
print ("")
print ("Type of 'train_X' is ", type(train_X))
print ("Shape of 'train_X' is %s" % (train_X.shape,))
print ("Type of 'train_Y' is ", type(train_Y))
print ("Shape of 'train_Y' is %s" % (train_Y.shape,))
# Plot
plt.figure(1)
plt.plot(train_X[0, :], ref_Y[0, :], 'ro', label="Original Data")
plt.plot(train_X[0, :], train_Y[0, :], 'bo', label="Training Data")
plt.axis('equal')
plt.legend(loc='lower right')
plt.show()
In [7]:
# Prepare for Linear Regression
# Parameters
training_epochs = 2000
display_step = 50
# Set Tensorflow Graph
X = tf.placeholder(tf.float32, name="input")
Y = tf.placeholder(tf.float32, name="output")
W = tf.Variable(np.random.randn(), name="weight")
b = tf.Variable(np.random.randn(), name="bias")
# Construct a Model
activation = tf.add(tf.mul(X, W), b)
# Define Error Measure and Optimizer
learning_rate = 0.01
cost = tf.reduce_mean(tf.pow(activation-Y, 2))
#learning_rate = 0.001
#cost = tf.sqrt(tf.reduce_mean(tf.pow(activation-Y, 2)))
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost) #Gradient Descent
"""
tf.reduce_sum()
tf.reduce_mean()
_____
tf.pow(Yhat, Y, 2)
tf.nn.softmax_cross_entropy_with_logits(Yhat, Y)
_____
tf.train.GradientDescentOptimizer(0.05).minimize(cost)
tf.train.RMSPropOptimizer(0.001, 0.9).minimize(cost)
"""
# Initializer
init = tf.initialize_all_variables()
In [12]:
# Run
sess = tf.Session()
# Initialize
sess.run(init)
for epoch in range(training_epochs):
for (x, y) in zip(train_X[0, :], train_Y[0, :]):
# print ("x: ", x, "y: ", y)
sess.run(optimizer, feed_dict={X:x, Y:y})
# Check cost
if (epoch % display_step == 0):
costval = sess.run(cost, feed_dict={X:train_X, Y:train_Y})
print ("Epoch:", "%04d" % (epoch+1), "cost=", "{:.5f}".format(costval))
Wtemp = sess.run(W)
btemp = sess.run(b)
print (" Wtemp is", "{:.4f}".format(Wtemp), "btemp is", "{:.4f}".format(btemp))
print (" Wref is", "{:.4f}".format(Wref), "bref is", "{:.4f}".format(bref))
# Final W and b
Wopt = sess.run(W)
bopt = sess.run(b)
fopt = f(train_X, Wopt,bopt)
In [14]:
# Plot Results
plt.figure(2)
plt.plot(train_X[0, :], ref_Y[0, :], 'ro', label='Original data')
plt.plot(train_X[0, :], train_Y[0, :], 'bo', label='Training data')
plt.plot(train_X[0, :], fopt[0, :], 'k-', label='Fitted Line')
plt.axis('equal')
plt.legend(loc='lower right')
plt.show()
In [ ]:
In [ ]:
In [ ]:
In [ ]:
In [ ]:
In [ ]:
In [ ]: