In [75]:

    

#Lab_3_Assignment_1_LASSO_RIDGE_REGULARISATION
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
import sys
from tensorflow.python.framework import ops


    

In [76]:

    

x_vals = np.linspace(-1, 1, 101)
# create a y value which is approximately linear but with some random noise
y_vals = 2 * trX + np.random.randn(*trX.shape) * 0.33


    

In [77]:

    

# clear out old graph
ops.reset_default_graph()

# Create graph
sess = tf.Session()


    

In [79]:

    

batch_size = 100

# Initialize placeholders
x_data = tf.placeholder(shape=[None, 1], dtype=tf.float32)
y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)

# make results reproducible
seed = 13
np.random.seed(seed)
tf.set_random_seed(seed)

# Create variables for linear regression
A = tf.Variable(tf.random_normal(shape=[1,1]))
#b = tf.Variable(tf.random_normal(shape=[1,1]))

# Declare model operations
model_output = tf.matmul(x_data, A)


    

In [80]:

    

# Specify 'Ridge' or 'LASSO'
regression_type = 'LASSO'


    

In [85]:

    

# Select appropriate loss function based on regression type

if regression_type == 'LASSO':
    # Declare Lasso loss function
    # Lasso Loss = L2_Loss + heavyside_step,
    # Where heavyside_step ~ 0 if A < constant, otherwise ~ 99
    lasso_param = tf.constant(0.9)
    heavyside_step = tf.truediv(1., tf.add(1., tf.exp(tf.multiply(-50., tf.subtract(A, lasso_param)))))
    regularization_param = tf.multiply(heavyside_step, 99.)
    loss = tf.add(tf.reduce_mean(tf.square(y_target - model_output)), regularization_param)

elif regression_type == 'Ridge':
    # Declare the Ridge loss function
    # Ridge loss = L2_loss + L2 norm of slope
    ridge_param = tf.constant(1.)
    ridge_loss = tf.reduce_mean(tf.square(A))
    loss = tf.expand_dims(tf.add(tf.reduce_mean(tf.square(y_target - model_output)), tf.multiply(ridge_param,ridge_loss)), 0)
    
else:
    print('Invalid regression_type parameter value',file=sys.stderr)


    

In [86]:

    

# Declare optimizer
my_opt = tf.train.GradientDescentOptimizer(0.001)
train_step = my_opt.minimize(loss)


    

In [88]:

    

# Initialize variables
init = tf.global_variables_initializer()
sess.run(init)

# Training loop
loss_vec = []
for i in range(1500):
    rand_index = np.random.choice(len(x_vals), size=batch_size)
    rand_x = np.transpose([x_vals[rand_index]])
    rand_y = np.transpose([y_vals[rand_index]])
    sess.run(train_step, feed_dict={x_data: rand_x, y_target: rand_y})
    temp_loss = sess.run(loss, feed_dict={x_data: rand_x, y_target: rand_y})
    loss_vec.append(temp_loss[0])
    if (i+1)%300==0:
        print('Step #' + str(i+1) + ' A = ' + str(sess.run(A)) )
        print('Loss = ' + str(temp_loss))
        print('\n')


    

    




Step #300 A = [[ 1.8155663]]
Loss = [[ 99.0916748]]


Step #600 A = [[ 1.84611189]]
Loss = [[ 99.09740448]]


Step #900 A = [[ 1.8716892]]
Loss = [[ 99.1035614]]


Step #1200 A = [[ 1.89144838]]
Loss = [[ 99.08739471]]


Step #1500 A = [[ 1.90643394]]
Loss = [[ 99.08901978]]

In [90]:

    

# Get the optimal coefficients
[slope] = sess.run(A)
#[y_intercept] = sess.run(b)

# Get best fit line
best_fit = []
for i in x_vals:
    best_fit.append(slope*i)


    

In [92]:

    

%matplotlib inline
# Plot the result
plt.plot(x_vals, y_vals, 'o', label='Data Points')
plt.plot(x_vals, best_fit, 'r-', label='Best fit line', linewidth=3)
plt.legend(loc='upper left')
plt.show()

# Plot loss over time
plt.plot(loss_vec, 'k-')
plt.title(regression_type + ' Loss per Generation')
plt.xlabel('Generation')
plt.ylabel('Loss')
plt.show()


    

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