Ridge regularization

The following is the complete code for ridge regularized regression to train the model in order to predict Boston house pricing:

num_outputs = y_train.shape[1]
num_inputs = X_train.shape[1]

x_tensor = tf.placeholder(dtype=tf.float32,
                          shape=[None, num_inputs], name='x')
y_tensor = tf.placeholder(dtype=tf.float32,
                          shape=[None, num_outputs], name='y')

w = tf.Variable(tf.zeros([num_inputs, num_outputs]),
                dtype=tf.float32, name='w')
b = tf.Variable(tf.zeros([num_outputs]),
                dtype=tf.float32, name='b')

model = tf.matmul(x_tensor, w) + b

ridge_param = tf.Variable(0.8, dtype=tf.float32)
ridge_loss = tf.reduce_mean(tf.square(w)) * ridge_param

loss = tf.reduce_mean(tf.square(model - y_tensor)) + ridge_loss

learning_rate = 0.001
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)

mse = tf.reduce_mean(tf.square(model - y_tensor))
y_mean = tf.reduce_mean(y_tensor)
total_error = tf.reduce_sum(tf.square(y_tensor - y_mean))
unexplained_error = tf.reduce_sum(tf.square(y_tensor - model))
rs = 1 - tf.div(unexplained_error, total_error)

num_epochs = 1500
loss_epochs = np.empty(shape=[num_epochs],dtype=np.float32)
mse_epochs = np.empty(shape=[num_epochs],dtype=np.float32)
rs_epochs = np.empty(shape=[num_epochs],dtype=np.float32)

mse_score = 0.0
rs_score = 0.0

with tf.Session() as tfs:
    tfs.run(tf.global_variables_initializer())
    for epoch in range(num_epochs):
        feed_dict = {x_tensor: X_train, y_tensor: y_train}
        loss_val, _ = tfs.run([loss, optimizer], feed_dict=feed_dict)
        loss_epochs[epoch] = loss_val

        feed_dict = {x_tensor: X_test, y_tensor: y_test}
        mse_score, rs_score = tfs.run([mse, rs], feed_dict=feed_dict)
        mse_epochs[epoch] = mse_score
        rs_epochs[epoch] = rs_score

print('For test data : MSE = {0:.8f}, R2 = {1:.8f} '.format(
    mse_score, rs_score))
 

We get the following result:

For test data : MSE = 30.64177132, R2 = 0.63988018 

Plotting the values of loss and MSE, we get the following plot for loss:

We get the following plot for R-squared:

Let's look at the combination of lasso and ridge regularization methods.