Tensorflow Dropout implementation, test accuracy = train accuracy and low, why? - tensorflow

Question

I have tried dropout implementation in Tensorflow.
I do know that dropout should be declared as a placeholder and keep_prob parameter during training and testing should be different. However still almost broke my brain trying to find why with dropout the accuracy is so low. When keep_drop = 1, the train accuracy 99%, test accuracy 85%, with keep_drop = 0.5, both train and test accuracy is 16% Any ideas where to look into, anyone? Thank you!
def forward_propagation(X, parameters, keep_prob):
"""
Implements the forward propagation for the model: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SOFTMAX
Arguments:
X -- input dataset placeholder, of shape (input size, number of examples)
parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3"
the shapes are given in initialize_parameters
Returns:
Z3 -- the output of the last LINEAR unit
"""
# Retrieve the parameters from the dictionary "parameters"
W1 = parameters['W1']
b1 = parameters['b1']
W2 = parameters['W2']
b2 = parameters['b2']
W3 = parameters['W3']
b3 = parameters['b3']
Z1 = tf.add(tf.matmul(W1,X),b1) # Z1 = np.dot(W1, X) + b1
A1 = tf.nn.relu(Z1) # A1 = relu(Z1)
A1 = tf.nn.dropout(A1,keep_prob) # apply dropout
Z2 = tf.add(tf.matmul(W2,A1),b2) # Z2 = np.dot(W2, a1) + b2
A2 = tf.nn.relu(Z2) # A2 = relu(Z2)
A2 = tf.nn.dropout(A2,keep_prob) # apply dropout
Z3 = tf.add(tf.matmul(W3,A2),b3) # Z3 = np.dot(W3,A2) + b3
return Z3
def model(X_train, Y_train, X_test, Y_test, learning_rate = 0.0001, lambd = 0.03, train_keep_prob = 0.5,
num_epochs = 800, minibatch_size = 32, print_cost = True):
"""
Implements a three-layer tensorflow neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SOFTMAX.
Arguments:
X_train -- training set, of shape (input size = 12288, number of training examples = 1080)
Y_train -- test set, of shape (output size = 6, number of training examples = 1080)
X_test -- training set, of shape (input size = 12288, number of training examples = 120)
Y_test -- test set, of shape (output size = 6, number of test examples = 120)
learning_rate -- learning rate of the optimization
lambd -- L2 regularization hyperparameter
train_keep_prob -- probability of keeping a neuron in hidden layer for dropout implementation
num_epochs -- number of epochs of the optimization loop
minibatch_size -- size of a minibatch
print_cost -- True to print the cost every 100 epochs
Returns:
parameters -- parameters learnt by the model. They can then be used to predict.
"""
ops.reset_default_graph() # to be able to rerun the model without overwriting tf variables
tf.set_random_seed(1) # to keep consistent results
seed = 3 # to keep consistent results
(n_x, m) = X_train.shape # (n_x: input size, m : number of examples in the train set)
n_y = Y_train.shape[0] # n_y : output size
costs = [] # To keep track of the cost
# Create Placeholders of shape (n_x, n_y)
X, Y = create_placeholders(n_x, n_y)
keep_prob = tf.placeholder(tf.float32)
# Initialize parameters
parameters = initialize_parameters()
# Forward propagation: Build the forward propagation in the tensorflow graph
Z3 = forward_propagation(X, parameters, keep_prob)
# Cost function: Add cost function to tensorflow graph
cost = compute_cost(Z3, Y, parameters, lambd)
# Backpropagation.
optimizer = tf.train.AdamOptimizer(learning_rate = learning_rate).minimize(cost)
# Initialize all the variables
init = tf.global_variables_initializer()
# Start the session to compute the tensorflow graph
with tf.Session() as sess:
# Run the initialization
sess.run(init)
# Do the training loop
for epoch in range(num_epochs):
epoch_cost = 0. # Defines a cost related to an epoch
num_minibatches = int(m / minibatch_size) # number of minibatches of size minibatch_size in the train set
seed = seed + 1
minibatches = random_mini_batches(X_train, Y_train, minibatch_size, seed)
for minibatch in minibatches:
# Select a minibatch
(minibatch_X, minibatch_Y) = minibatch
# IMPORTANT: The line that runs the graph on a minibatch.
# Run the session to execute the "optimizer" and the "cost", the feedict should contain a minibatch for (X,Y).
_ , minibatch_cost = sess.run([optimizer, cost], feed_dict={X: minibatch_X, Y: minibatch_Y, keep_prob: train_keep_prob})
epoch_cost += minibatch_cost / num_minibatches
# Print the cost every epoch
if print_cost == True and epoch % 100 == 0:
print ("Cost after epoch %i: %f" % (epoch, epoch_cost))
if print_cost == True and epoch % 5 == 0:
costs.append(epoch_cost)
# plot the cost
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per tens)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
# lets save the parameters in a variable
parameters = sess.run(parameters)
print ("Parameters have been trained!")
# Calculate the correct predictions
correct_prediction = tf.equal(tf.argmax(Z3), tf.argmax(Y))
# Calculate accuracy on the test set
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
print ("Train Accuracy:", accuracy.eval({X: X_train, Y: Y_train, keep_prob: 1.0}))
print ("Test Accuracy:", accuracy.eval({X: X_test, Y: Y_test, keep_prob: 1.0}))
return parameters

Answer 1

The algo is correct. It is just the keep_prob = 0.5 is too low.
Managed to get 87% accuracy on the test set with the following hyperparameters:
learning_rate = 0.00002, lambd = 0.03, train_keep_prob = 0.90, num_epochs = 1500, minibatch_size = 32,

Answer 2

In the first case your model was overfitting to the data, hence the large difference between the train and test accuracy. Dropout is a regularization technique to reduce the variance of the model by reducing the effect of particular nodes and hence prevent overfitting. But keeping the keep_prob = 0.5(too low) weakens the model and hence it underfits severely to the data, giving an accuracy as low as 16%. You should iterate by gradually decreasing the keep_prob value untill you find a suitable value.