Mini batch stochastic gradient descent - machine-learning

My question is what changes should be made to SGD algorithm to implement mini-batch SGD algorithm.
In the book, Machine Learning by Tom Mitchell, the GD, and SGD algorithms are explained very well. Here is a snippet of the book for SGD backpropagation algorithm:
I know that the difference between SGD and mini-batch SGD is that in the former we use one training example to update weights in each iteration (of the outer while-loop), while in the latter, a batch of training examples should be used in each iteration. But I still can't figure how the below algorithm should be changed to account for this change.
Here is what I think it should look like, but can't confirm this from several tutorials I followed on the web.
Until the termination condition is met, Do
batch <- get next batch
For each <x,t> in batch, Do
1- Propagate the input forward through the network.
2- d_k += o_k(1 - o_k)(t_k - o_k)
3- d_h += o_h(1 - o_h)sum(w_kh * d_k)
For each network weight w_ij, Do
w_ji += etha * d_j * x_ij
Any help is much appreciated!

Related

What is the difference between these backward training methods in Pytorch?

I am a 3-month DL freshman who is doing small NLP projects with Pytorch.
Recently I am trying to reappear a GAN network introduced by a paper, using my own text data, to generate some specific kinds of question sentences.
Here is some background... If you have no time or interest about it, just kindly read the following question is OK.
As that paper says, the generator is firstly trained normally with normal question data to make that the output at least looks like a real question. Then by using an auxiliary classifier's result (of classifying the outputs), the generator is trained again to just generate the specific (several unique categories) questions.
However, as the paper do not reveal its code, I have to do the code all myself. I have these three training thoughts, but I do not know their differences, could you kindly tell me about it?
If they have almost the same effect, could you tell me which is more recommended in Pytorch's grammar? Thank you very much!
Suppose the discriminator loss to generator is loss_G_D, the classifier loss to generator is loss_G_C, and loss_G_D and loss_G_C has the same shape, i.e. [batch_size, loss value], then what is the difference?
1.
optimizer.zero_grad()
loss_G_D = loss_func1(discriminator(generated_data))
loss_G_C = loss_func2(classifier(generated_data))
loss = loss_G+loss_C
loss.backward()
optimizer.step()
optimizer.zero_grad()
loss_G_D = loss_func1(discriminator(generated_data))
loss_G_D.backward()
loss_G_C = loss_func2(classifier(generated_data))
loss_G_C.backward()
optimizer.step()
optimizer.zero_grad()
loss_G_D = loss_func1(discriminator(generated_data))
loss_G_D.backward()
optimizer.step()
optimizer.zero_grad()
loss_G_C = loss_func2(classifier(generated_data))
loss_G_C.backward()
optimizer.step()
Additional info: I observed that the classifier's classification loss is always very big compared with generator's loss, like -300 vs 3. So maybe the third one is better?
First of all:
loss.backward() backpropagates the error and assigns a gradient for every parameter along the way that has requires_grad=True.
optimizer.step() updates the model parameters using their stored gradients
optimizer.zero_grad() sets the gradients to 0, so that you can backpropagate your loss and update your model parameters for each batch without interfering with other batches.
1 and 2 are quite similar, but if your model uses batch statistics or you have an adaptive optimizer they will probably perform differently. However, for instance, if your model doesn't use batch statistics and you have a plain old SGD optimizer, they will produce the same result, even though 1 would be faster since you do the backprop only once.
3 is a completely different case, since you update your model parameters with loss_G_D.backward() and optimizer.step() before processing and backpropagating loss_G_C.
Given all of these, it's up to you which one to choose depending on your application.

training loss increases over time despite of a tiny learning rate

I'm playing with CIFAR-10 dataset using ResNet-50 on Keras with Tensorflow backend, but I ran into a very strange training pattern, where the model loss decreased first, and then started to increase until it plateaued/stuck at a single value due to almost 0 learning rate. Correspondingly, the model accuracy increased first, and then started to decrease until it plateaued at 10% (aka random guess). I wonder what is going wrong?
Typically this U shaped pattern happens with a learning rate that is too large (like this post), but it is not the case here. This pattern also doesn't' look like a classic "over-fitting" as both the training and validation loss increase over time. In the answer to the above linked post, someone mentioned that if Adam optimizer is used, loss may explode under small learning rate when local minimum is exceeded, I'm not sure I can follow what is said there, and also I'm using SGD with weight decay instead of Adam.
Specifically for the training set up, I used resent50 with random initialization, SGD optimizer with 0.9 momentum and a weight decay of 0.0001 using decoupled weight decay regularization, batch-size 64, initial learning_rate 0.01 which declined by a factor of 0.5 with each 10 epochs of non-decreasing validation loss.
base_model = tf.keras.applications.ResNet50(include_top=False,
weights=None,pooling='avg',
input_shape=(32,32,3))
prediction_layer = tf.keras.layers.Dense(10)
model = tf.keras.Sequential([base_model,
prediction_layer])
SGDW = tfa.optimizers.extend_with_decoupled_weight_decay(tf.keras.optimizers.SGD)
optimizer = SGDW(weight_decay=0.0001, learning_rate=0.01, momentum=0.9)
loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),
metrics=["accuracy"])
reduce_lr= tf.keras.callbacks.ReduceLROnPlateau(monitor='val_loss',factor=0.5, patience=10)
model.compile(optimizer=optimizer,
loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),
metrics=["accuracy"])
model.fit(train_batches, epochs=250,
validation_data=validation_batches,
callbacks=[reduce_lr])

How to update batch weights in back propagation

How gradient descent algorithm updates the batch weights in the back propagation method?
Thanks in advance ...
It is really easy once you understand the algorithm.
New Weights = Old Weights - learning-rate x Partial derivatives of loss function w.r.t. parameters
Let's consider a neural network with two inputs, two hidden neurons, two output neurons.
First, introduce weights and bias to your network. Then, compute total net input for hidden layer, as such
net_{h1} = w_1 * i_1 + w_2 * i_2 + b_1 * 1
Do the same for all other hidden layers.
Next, we can now calculate the error for each output neuron using the squared error function and sum them to get the total error.
Hereinafter, you will have to calculate the partial derivative of the total network error with respect to the previous weights, to find out how each weights affects the network. I have included a visual to help with your understanding.
I strongly suggest you go through this beginner friendly introduction to back-propagation to have a firm grasp of the concept. I hope my beginner post help you get started in the journey of Machine Learning!

How to find if a data set can train a neural network?

I'm a newbie to machine learning and this is one of the first real-world ML tasks challenged.
Some experimental data contains 512 independent boolean features and a boolean result.
There are about 1e6 real experiment records in the provided data set.
In a classic XOR example all 4 out of 4 possible states are required to train NN. In my case its only 2^(10-512) = 2^-505 which is close to zero.
I have no more information about the data nature, just these (512 + 1) * 1e6 bits.
Tried NN with 1 hidden layer on available data. Output of the trained NN on the samples even from the training set are always close to 0, not a single close to "1". Played with weights initialization, gradient descent learning rate.
My code utilizing TensorFlow 1.3, Python 3. Model excerpt:
with tf.name_scope("Layer1"):
#W1 = tf.Variable(tf.random_uniform([512, innerN], minval=-2/512, maxval=2/512), name="Weights_1")
W1 = tf.Variable(tf.zeros([512, innerN]), name="Weights_1")
b1 = tf.Variable(tf.zeros([1]), name="Bias_1")
Out1 = tf.sigmoid( tf.matmul(x, W1) + b1)
with tf.name_scope("Layer2"):
W2 = tf.Variable(tf.random_uniform([innerN, 1], minval=-2/512, maxval=2/512), name="Weights_2")
#W2 = tf.Variable(tf.zeros([innerN, 1]), name="Weights_2")
b2 = tf.Variable(tf.zeros([1]), name="Bias_2")
y = tf.nn.sigmoid( tf.matmul(Out1, W2) + b2)
with tf.name_scope("Training"):
y_ = tf.placeholder(tf.float32, [None,1])
cross_entropy = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(
labels = y_, logits = y)
)
train_step = tf.train.GradientDescentOptimizer(0.005).minimize(cross_entropy)
with tf.name_scope("Testing"):
# Test trained model
correct_prediction = tf.equal( tf.round(y), tf.round(y_))
# ...
# Train
for step in range(500):
batch_xs, batch_ys = Datasets.train.next_batch(300, shuffle=False)
_, my_y, summary = sess.run([train_step, y, merged_summaries],
feed_dict={x: batch_xs, y_: batch_ys})
I suspect two cases:
my fault – bad NN implementation, wrong architecture;
bad data. Compared to XOR example, incomplete training data would result in a failing NN. However, the training examples fed to the trained NN are supposed to give right predictions, aren't they?
How to evaluate if it is possible at all to train a neural network (a 2-layer perceptron) on the provided data to forecast the result? A case of aceptable set would be the XOR example. Opposed to some random noise.
There are only ad hoc ways to know if it is possible to learn a function with a differentiable network from a dataset. That said, these ad hoc ways do usually work. For example, the network should be able to overfit the training set without any regularisation.
A common technique to gauge this is to only fit the network on a subset of the full dataset. Check that the network can overfit to that, then increase the size of the subset, and increase the size of the network as well. Unfortunately, deciding whether to add extra layers or add more units in a hidden layer is an arbitrary decision you'll have to make.
However, looking at your code, there are a few things that could be going wrong here:
Are your outputs balanced? By that I mean, do you have the same number of 1s as 0s in the dataset targets?
Your initialisation in the first layer is all zeros, the gradient to this will be zero, so it can't learn anything (although, you have a real initialisation above it commented out).
Sigmoid nonlinearities are more difficult to optimise than simpler nonlinearities, such as ReLUs.
I'd recommend using the built-in definitions for layers in Tensorflow to not worry about initialisation, and switching to ReLUs in any hidden layers (you need sigmoid at the output for your boolean target).
Finally, deep learning isn't actually very good at most "bag of features" machine learning problems because they lack structure. For example, the order of the features doesn't matter. Other methods often work better, but if you really want to use deep learning then you could look at this recent paper, showing improved performance by just using a very specific nonlinearity and weight initialisation (change 4 lines in your code above).

understanding test and validation set usage for early stop and model selection

I implemented an ANN (1 hidden layer of 64 units, learning rate = 0.001, epsilon = 0.001, iters = 500) with pythons OpenCV module. Train error ~ 3% and test error ~ 12%
In order to improve the accruacy/ generalisation of my NN I decided to proceed by- implementing model selection (of #hidden units and learning rate) to get an accurate value of hyperparameters and plotting learning curves to determine if more data is needed (currently have 2.5k).
Having read some sources regarding NN training and model selection, I'm very confused on the following matter -
1) In order to perform model selection, I know the following needs to be done-
create set possibleHiddenUnits {4, 8, 16, 32, 64}
randomly select Tr & Va sets from the total set of Tr + Va with some split e.g. 80/20
foreach ele in possibleHiddenUnits
(*) compute weights for the NN using backpropagation and an iterative optimisation algorithm like Gradient Descent (where we provide the termination criteria in the form of number of iterations / epsilon)
compute Validation set error using these trained weights
select the number of hidden units which min Va set error
Alternatively, I believe we can also use k-fold cross validation.
a. how do you decide what the number of iterations/ epsilon for GD should be?
b. does 1 iteration out of x iterations of GD (where the entire training set is used to compute the gradients of cost wrt weights through backprop) constitute an 'epoch'?
2) Sources (whats is the difference between train, validation and test set, in neural networks? and How to use k-fold cross validation in a neural network) mention that the training for a NN is done in the following way as it prevents over-fitting
for each epoch
for each training data instance
propagate error through the network
adjust the weights
calculate the accuracy over training data
for each validation data instance
calculate the accuracy over the validation data
if the threshold validation accuracy is met
exit training
else
continue training
a. I believe this method should be executed once the model selection has been done. But then how do we avoid overfitting of the model in step (*) of the model selection process above?
b. Am I right in assuming that one epoch constitues one iteration of training where weights are calculated using the entire Tr set through GD + backprop and GD involves x (>1) iters over the entire Tr set to calculate the weights ?
Also, out off 1b and 2b which is correct?
This is more of a comment but since I cant make comments yet I write it here. Have you tried other methods like l2 regularization or dropout? I dont know a lot about model selection but dropout has a very similiar effect like taking lots of models and averaging them. Normaly dropout should do the trick and you wont have problems with overfitting anymore.

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