Develop Reference

Finding patterns in time series with PyTorch

I started PyTorch with image recognition. Now I want to test (very basically) with pure NumPy arrays. I struggle with getting the setup to work, so basically I have vectors with values between 0 and 1 (normalized curves). Those vectors are always of length 1500 and I want to find e.g. "high values at the beginning" or "sine wave-like function", "convex", "concave" etc. stuff like that, so just shapes of those curves.
My training set consists of many vectors with their classes; I have chosen 7 classes. The net should be trained to classify a vector into one or more of those 7 classes (not one hot).
I'm struggling with multiple issues, but first my very basic Net
class Net(nn.Module):
def __init__(self, input_dim, hidden_dim, layer_dim, output_dim):
super(Net, self).__init__()
self.hidden_dim = hidden_dim
self.layer_dim = layer_dim
self.rnn = nn.RNN(input_dim, hidden_dim, layer_dim)
self.fc = nn.Linear(self.hidden_dim, output_dim)
def forward(self, x):
h0 = torch.zeros(self.layer_dim, x.size(1), self.hidden_dim).requires_grad_()
out, h0 = self.rnn(x, h0.detach())
out = out[:, -1, :]
out = self.fc(out)
return out
network = Net(1500, 70, 20, 7)
optimizer = optim.SGD(network.parameters(), lr=learning_rate, momentum=momentum)
This is just a copy-paste from an RNN demo. Here is my first issue. Is an RNN the right choice? It is a time series, but then again it is an image recognition problem when plotting the curve.
Now, this here is an attempt to batch the data. The data object contains all training curves together with the correct classifiers.
def train(epoch):
network.train()
network.float()
batching = True
index = 0
# monitor the cummulative loss for an epoch
cummloss = []
# start batching some curves
while batching:
optimizer.zero_grad()
# here I start clustering come curves to a batch and normalize the curves
_input = []
batch_size = min(len(data)-1, index+batch_size_train) - index
for d in data[index:min(len(data)-1, index+batch_size_train)]:
y = np.array(d['data']['y'], dtype='d')
y = np.multiply(y, y.max())
y = y[0:1500]
y = np.pad(y, (0, max(1500-len(y), 0)), 'edge')
if len(_input) == 0:
_input = y
else:
_input = np.vstack((_input, y))
input = torch.from_numpy(_input).float()
input = torch.reshape(input, (1, batch_size, len(y)))
target = np.zeros((1,7))
# the correct classes have indizes, to I create a vector with 1 at the correct locations
for _index in np.array(d['classifier']):
target[0,_index-1] = 1
target = torch.from_numpy(target)
# get the result form the network
output = network(input)
# is this a good loss function?
loss = F.l1_loss(output, target)
loss.backward()
cummloss.append(loss.item())
optimizer.step()
index = index + batch_size_train
if index > len(data):
print(np.mean(cummloss))
batching = False
for e in range(1, n_epochs):
print('Epoch: ' + str(e))
train(0)
The problem I'm facing right now is, the loss doesn't change very little, even with hundreds of epochs.
Are there existing examples of this kind of problem? I didn't find any, just pure png/jpg image recognition. When I convert the curves to png then I have a little issue to train a net, I took densenet and it worked just fine but it seems to be super overkill for this simple task.

This is just a copy-paste from an RNN demo. Here is my first issue. Is an RNN the right choice?
In theory what model you choose does not matter as much as "How" you formulate your problem.
But in your case the most obvious limitation you're going to face is your sequence length: 1500. RNN store information across steps and typically runs into trouble over long sequence with vanishing or exploding gradient.
LSTM net have been developed to circumvent this limitations with memory cell, but even then in the case of long sequence it will still be limited by the amount of information stored in the cell.
You could try using a CNN network as well and think of it as an image.
Are there existing examples of this kind of problem?
I don't know but I might have some suggestions : If I understood your problem correctly, you're going from a (1500, 1) input to a (7,1) output, where 6 of the 7 positions are 0 except for the corresponding class where it's 1.
I don't see any activation function, usually when dealing with multi class you don't use the output of the dense layer to compute the loss you apply a normalizing function like softmax and then you can compute the loss.

From your description of features you have in the form of sin like structures, the closes thing that comes to mind is frequency domain. As such, if you have and input image, just transform it to the frequency domain by a Fourier transform and use that as your feature input.
Might be best to look for such projects on the internet, one such project that you might want to read the research paper or video from this group (they have some jupyter notebooks for you to try) or any similar works. They use the furrier features, that go though a multi layer perceptron (MLP).
I am not sure what exactly you want to do, but seems like a classification task, you would use RNN if you want your neural network to work with a sequence. To me it seems like the 1500 dimensions are independent, and as such can be just treated as input.
Regarding the last layer, for a classification problem it usually is a probability distribution obtained by applying softmax (if only the classification is distinct - i.e. probability sums up to 1), in which, given an input, the net gives a probability of it being from each class. If we are predicting multiple classes we are going to use sigmoid as the last layer of the neural network.
Regarding your loss, there are many losses you can try and see if they are better. Once again, for different features you have to know what exactly is the measurement of distance (a.k.a. how different 2 things are). Check out this website, or just any loss function explanations on the net.
So you should try a simple MLP on top of fourier features as a starting point, assuming that is your feature vector.

Image Recognition is different from Time-Series data. In the imaging domain your data-set might have more similarity with problems like Activity-Recognition, Video-Recognition which have temporal component. So, I'd recommend looking into some models for those.
As for the current model, I'd recommend using LSTM instead of RNN. And also for classification you need to use an activation function in your final layer. This should softmax with cross entropy based loss or sigmoid with MSE loss.
Keras has a Timedistributed model which makes it easy to handle time components. You can use a similar approach with Pytorch by applying linear layers followed by LSTM.
Look into these for better undertsanding ::
Activity Recognition : https://www.narayanacharya.com/vision/2019-12-30-Action-Recognition-Using-LSTM
https://discuss.pytorch.org/t/any-pytorch-function-can-work-as-keras-timedistributed/1346
How to implement time-distributed dense (TDD) layer in PyTorch
Activation Function ::
https://pytorch.org/docs/stable/generated/torch.nn.Softmax.html

How can I compare weights of different Keras models?

I've saved numbers of models in .h5 format. I want to compare their characteristics such as weight.
I don't have any Idea how I can appropriately compare them specially in the form of tables and figures.
Thanks in advance.

Weight-introspection is a fairly advanced endeavor, and requires model-specific treatment. Visualizing weights is a largely technical challenge, but what you do with that information's a different matter - I'll address largely the former, but touch upon the latter.
Update: I also recommend See RNN for weights, gradients, and activations visualization.
Visualizing weights: one approach is as follows:
Retrieve weights of layer of interest. Ex: model.layers[1].get_weights()
Understand weight roles and dimensionality. Ex: LSTMs have three sets of weights: kernel, recurrent, and bias, each serving a different purpose. Within each weight matrix are gate weights - Input, Cell, Forget, Output. For Conv layers, the distinction's between filters (dim0), kernels, and strides.
Organize weight matrices for visualization in a meaningful manner per (2). Ex: for Conv, unlike for LSTM, feature-specific treatment isn't really necessary, and we can simply flatten kernel weights and bias weights and visualize them in a histogram
Select visualization method: histogram, heatmap, scatterplot, etc - for flattened data, a histogram is the best bet
Interpreting weights: a few approaches are:
Sparsity: if weight norm ("average") is low, the model is sparse. May or may not be beneficial.
Health: if too many weights are zero or near-zero, it's a sign of too many dead neurons; this can be useful for debugging, as once a layer's in such a state, it usually does not revert - so training should be restarted
Stability: if weights are changing greatly and quickly, or if there are many high-valued weights, it may indicate impaired gradient performance, remedied by e.g. gradient clipping or weight constraints
Model comparison: there isn't a way for simply looking at two weights from separate models side-by-side and deciding "this is the better one"; analyze each model separately, for example as above, then decide which one's ups outweigh downs.
The ultimate tiebreaker, however, will be validation performance - and it's also the more practical one. It goes as:
Train model for several hyperparameter configurations
Select one with best validation performance
Fine-tune that model (e.g. via further hyperparameter configs)
Weight visualization should be mainly kept as a debugging or logging tool - as, put simply, even with our best current understanding of neural networks one cannot tell how well the model will generalize just by looking at the weights.
Suggestion: also visualize layer outputs - see this answer and sample output at bottom.
Visual example:
from tensorflow.keras.layers import Input, Conv2D, Dense, Flatten
from tensorflow.keras.models import Model
ipt = Input(shape=(16, 16, 16))
x = Conv2D(12, 8, 1)(ipt)
x = Flatten()(x)
out = Dense(16)(x)
model = Model(ipt, out)
model.compile('adam', 'mse')
X = np.random.randn(10, 16, 16, 16) # toy data
Y = np.random.randn(10, 16) # toy labels
for _ in range(10):
model.train_on_batch(X, Y)
def get_weights_print_stats(layer):
W = layer.get_weights()
print(len(W))
for w in W:
print(w.shape)
return W
def hist_weights(weights, bins=500):
for weight in weights:
plt.hist(np.ndarray.flatten(weight), bins=bins)
W = get_weights_print_stats(model.layers[1])
# 2
# (8, 8, 16, 12)
# (12,)
hist_weights(W)
Conv1D outputs visualization: (source)

To compare weights of two models, I vectorize model weights (i.e., create 1D array) for each model. Then, I calculate the percent difference between respective weights and construct a histogram of these percent differences. If all values are close to zero, there is suggestion (but not proof) that the models are practically the same. This is just one approach out of many for comparing models using their weights.
As an aside, I will note that I use this method when I want some indication that my model has converged on a global, rather than local, minimum. I will train models with several different initializations. If all the initializations result in convergence to the same weights, it suggests that the minimum is a global minimum.

Adding Dropout to testing/inference phase

I've trained the following model for some timeseries in Keras:
input_layer = Input(batch_shape=(56, 3864))
first_layer = Dense(24, input_dim=28, activation='relu',
activity_regularizer=None,
kernel_regularizer=None)(input_layer)
first_layer = Dropout(0.3)(first_layer)
second_layer = Dense(12, activation='relu')(first_layer)
second_layer = Dropout(0.3)(second_layer)
out = Dense(56)(second_layer)
model_1 = Model(input_layer, out)
Then I defined a new model with the trained layers of model_1 and added dropout layers with a different rate, drp, to it:
input_2 = Input(batch_shape=(56, 3864))
first_dense_layer = model_1.layers[1](input_2)
first_dropout_layer = model_1.layers[2](first_dense_layer)
new_dropout = Dropout(drp)(first_dropout_layer)
snd_dense_layer = model_1.layers[3](new_dropout)
snd_dropout_layer = model_1.layers[4](snd_dense_layer)
new_dropout_2 = Dropout(drp)(snd_dropout_layer)
output = model_1.layers[5](new_dropout_2)
model_2 = Model(input_2, output)
Then I'm getting the prediction results of these two models as follow:
result_1 = model_1.predict(test_data, batch_size=56)
result_2 = model_2.predict(test_data, batch_size=56)
I was expecting to get completely different results because the second model has new dropout layers and theses two models are different (IMO), but that's not the case. Both are generating the same result. Why is that happening?

As I mentioned in the comments, the Dropout layer is turned off in inference phase (i.e. test mode), so when you use model.predict() the Dropout layers are not active. However, if you would like to have a model that uses Dropout both in training and inference phase, you can pass training argument when calling it, as suggested by François Chollet:
# ...
new_dropout = Dropout(drp)(first_dropout_layer, training=True)
# ...
Alternatively, If you have already trained your model and now want to use it in inference mode and keep the Dropout layers (and possibly other layers which have different behavior in training/inference phase such as BatchNormalization) active, you can define a backend function that takes the model's inputs as well as Keras learning phase:
from keras import backend as K
func = K.function(model.inputs + [K.learning_phase()], model.outputs)
# to use it pass 1 to set the learning phase to training mode
outputs = func([input_arrays] + [1.])

your question has a simple solution in the latest version of Tensorflow. you can set the training argument of the call method to true.
you can run a code like the below code:
model(input,training=True)
by using training=True TensorFlow automatically applies the Dropout layer in inference mode.

As there are already some working code solutions above, I will simply add a few more details regarding dropout during inference to prevent confusion.
Based on the original paper, Dropout layers play the role of turning off (setting gradients to zero) the neuron nodes during training to reduce overfitting. However, once we finish off with training and start testing the model, we do not 'touch' any neurons, thus, all the units are considered to make the decision when inferencing. This causes previously 'dead' neuron weights to be large than expected due to the usage of Dropout. To prevent this, a scaling factor is applied to balance the network node. To be more precise, if a unit is retained with probability p during training, the outgoing weights of that unit are multiplied by p during the prediction stage.

TimeDistributed layer and return sequences etc for LSTM in Keras

Sorry I am new to RNN. I have read this post on TimeDistributed layer.
I have reshaped my data in to Keras requried [samples, time_steps, features]: [140*50*19], which means I have 140 data points, each has 50 time steps, and 19 features. My output is shaped [140*50*1]. I care more about the last data point's accuracy. This is a regression problem.
My current code is :
x = Input((None, X_train.shape[-1]) , name='input')
lstm_kwargs = { 'dropout_W': 0.25, 'return_sequences': True, 'consume_less': 'gpu'}
lstm1 = LSTM(64, name='lstm1', **lstm_kwargs)(x)
output = Dense(1, activation='relu', name='output')(lstm1)
model = Model(input=x, output=output)
sgd = SGD(lr=0.00006, momentum=0.8, decay=0, nesterov=False)
optimizer = sgd
model.compile(optimizer=optimizer, loss='mean_squared_error')
My questions are:
My case is many-to-many, so I need to use return_sequences=True? How about if I only need the last time step's prediction, it would be many-to-one. So I need to my output to be [140*1*1] and return_sequences=False?
Is there anyway to enhance my last time points accuracy if I use many-to-many? I care more about it than the other points accuracy.
I have tried to use TimeDistributed layer as
output = TimeDistributed(Dense(1, activation='relu'), name='output')(lstm1)
the performance seems to be worse than without using TimeDistributed layer. Why is this so?
I tried to use optimizer=RMSprop(lr=0.001). I thought RMSprop is supposed to stabilize the NN. But I was never able to get good result using RMSprop.
How do I choose a good lr and momentum for SGD? I have been testing on different combinations manually. Is there a cross validation method in keras?

So:
Yes - return_sequences=False makes your network to output only a last element of sequence prediction.
You could define the output slicing using the Lambda layer. Here you could find an example on how to do this. Having the output sliced you can provide the additional output where you'll feed the values of the last timestep.
From the computational point of view these two approaches are equivalent. Maybe the problem lies in randomness introduced by weight sampling.
Actually - using RMSProp as a first choice for RNNs is a rule of thumb - not a general proved law. Moreover - it is strongly adviced not to change it's parameters. So this might cause the problems. Another thing is that LSTM needs a lot of time to stabalize. Maybe you need to leave it for more epochs. Last thing - is that maybe your data could favour another activation function.
You could use a keras.sklearnWrapper.

Backpropagation with Rectified Linear Units

I have written some code to implement backpropagation in a deep neural network with the logistic activation function and softmax output.
def backprop_deep(node_values, targets, weight_matrices):
delta_nodes = node_values[-1] - targets
delta_weights = delta_nodes.T.dot(node_values[-2])
weight_updates = [delta_weights]
for i in xrange(-2, -len(weight_matrices)- 1, -1):
delta_nodes = dsigmoid(node_values[i][:,:-1]) * delta_nodes.dot(weight_matrices[i+1])[:,:-1]
delta_weights = delta_nodes.T.dot(node_values[i-1])
weight_updates.insert(0, delta_weights)
return weight_updates
The code works well, but when I switched to ReLU as the activation function it stopped working. In the backprop routine I only change the derivative of the activation function:
def backprop_relu(node_values, targets, weight_matrices):
delta_nodes = node_values[-1] - targets
delta_weights = delta_nodes.T.dot(node_values[-2])
weight_updates = [delta_weights]
for i in xrange(-2, -len(weight_matrices)- 1, -1):
delta_nodes = (node_values[i]>0)[:,:-1] * delta_nodes.dot(weight_matrices[i+1])[:,:-1]
delta_weights = delta_nodes.T.dot(node_values[i-1])
weight_updates.insert(0, delta_weights)
return weight_updates
However, the network no longer learns, and the weights quickly go to zero and stay there. I am totally stumped.

Although I have determined the source of the problem, I'm going to leave this up in case it might be of benefit to someone else.
The problem was that I did not adjust the scale of the initial weights when I changed activation functions. While logistic networks learn very well when node inputs are near zero and the logistic function is approximately linear, ReLU networks learn well for moderately large inputs to nodes. The small weight initialization used in logistic networks is therefore not necessary, and in fact harmful. The behavior I was seeing was the ReLU network ignoring the features and attempting to learn the bias of the training set exclusively.
I am currently using initial weights distributed uniformly from -.5 to .5 on the MNIST dataset, and it is learning very quickly.