I am messing around with LSTMs and have a conceptual question. I created a matrix of bogus data on the following rules:
For each 1-D list in the matrix:
If previous element is less than 10, then this next element is the previous one plus 1.
Else, this element is sin(previous element)
This way, it is a sequence that is pretty simply based on the previous information. I set up an LSTM to learn the recurrence and ran it to train on the lists one at a time. I have an LSTM layer followed by a fully connected feed-forward layer. It learns the +1 step very easily, but has trouble with the sin step. It will seemingly pick a random number between -1 and 1 when making the next element when the previous one was greater than 10. My question is this: is the training only modifying the variables in my fully connected feed forward layer? Is that why it can't learn the non-linear sin function?
Here's the code snippet in question:
lstm = rnn_cell.LSTMCell(lstmSize)
y_ = tf.placeholder(tf.float32, [None, OS])
outputs, state = rnn.rnn(lstm, x, dtype=tf.float32)
outputs = tf.transpose(outputs, [1, 0, 2])
last = tf.gather(outputs, int(outputs.get_shape()[0]) - 1)
weights = tf.Variable(tf.truncated_normal([lstmSize, OS]))
bias = tf.Variable(tf.constant(0.1, shape=[OS]))
y = tf.nn.elu(tf.matmul(last, weights) + bias)
error = tf.reduce_mean(tf.square(tf.sub(y_, y)))
train_step = tf.train.AdamOptimizer(learning_rate=1e-3).minimize(error)
The error and shape organization seems to be correct, at least in the sense that it does learn the +1 step quickly without crashing. Shouldn't the LSTM be able to handle the non-linear sin function? It seems almost trivially easy, so my guess is that I set something up wrong and the LSTM isn't learning anything.
Related
Hi I am developing a neural network model using keras.
code
def base_model():
# Initialising the ANN
regressor = Sequential()
# Adding the input layer and the first hidden layer
regressor.add(Dense(units = 4, kernel_initializer = 'he_normal', activation = 'relu', input_dim = 7))
# Adding the second hidden layer
regressor.add(Dense(units = 2, kernel_initializer = 'he_normal', activation = 'relu'))
# Adding the output layer
regressor.add(Dense(units = 1, kernel_initializer = 'he_normal'))
# Compiling the ANN
regressor.compile(optimizer = 'adam', loss = 'mse', metrics = ['mae'])
return regressor
I have been reading about which kernel_initializer to use and came across the link- https://towardsdatascience.com/hyper-parameters-in-action-part-ii-weight-initializers-35aee1a28404
it talks about glorot and he initializations. I have tried with different intilizations for weights, but all of them give the same results. I want to understand how important is it do a proper initialization?
Thanks
I'll give you an explanation of how much weights initialisation is important.
Let's suppose our NN has an input layer with 1000 neurons, and suppose we start to initialise weights as they are normal distributed with mean 0 and variance 1 ().
At the second layer, we assume that only 500 first layer's neurons are activated, while the other 500 not.
The neuron's input of the second layer z will be the sum of :
so, it will be even normal distributed but with variance .
This means its value will be |z| >> 1 or |z| << 1, so neurons will saturate. The network will learn slowly at all.
A solution is to initialise weights as where is the number of the inputs of the first layer. In this way z will be and so less spreader, consequently neurons are less prone to saturate.
This trick can help as a start but in deep neural networks, due to the presence of hidden multi-layers, the weights initialisation should be done at each layer. A method may be using the batch normalization
Besides this from your code I can see you'v chosen as cost function the MSE, so it is a quadratic cost function. I don't know if your problem is a classification one, but if this is the case I suggest you to use a cross-entropy function as cost function for increasing the learning rate of your network.
I have a similar open question here on Cross Validated (though not implementation focused, which I intend this question to be, so I think they are both valid).
I'm working on a project that uses sensors to monitor a persons GPS location. The coordinates will then be converted to a simple-grid representation. What I want to try and do is after recording a users routes, train a neural network to predict the next coordinates, i.e. take the example below where a user repeats only two routes over time, Home->A and Home->B.
I want to train an RNN/LSTM with sequences of varying lengths e.g. (14,3), (13,3), (12,3), (11,3), (10,3), (9,3), (8,3), (7,3), (6,3), (5,3), (4,3), (3,3), (2,3), (1,3) and then also predict with sequences of varying lengths e.g. for this example route if I called
route = [(14,3), (13,3), (12,3), (11,3), (10,3)] //pseudocode
pred = model.predict(route)
pred should give me (9,3) (or ideally even a longer prediction e.g. ((9,3), (8,3), (7,3), (6,3), (5,3), (4,3), (3,3), (2,3), (1,3))
How do I feed such training sequences to the init and forward operations identified below?
self.rnn = nn.RNN(input_size, hidden_dim, n_layers, batch_first=True)
out, hidden = self.rnn(x, hidden)
Also, should the entire route be a tensor or each set of coordinates within the route a tensor?
I'm not very experienced with RNNs, but I'll give it a try.
A few things to pay attention to before we start:
1. Your data is not normalized.
2. The output prediction you want (even after normalization) is not bounded to [-1, 1] range and therefore you cannot have tanh or ReLU activations acting on the output predictions.
To address your problem, I propose a recurrent net that given a current state (2D coordinate) predicts the next state (2D coordinates). Note that since this is a recurrent net, there is also a hidden state associated with each location. At first, the hidden state is zero, but as the net sees more steps, it updates its hidden state.
I propose a simple net to address your problem. It has a single RNN layer with 8 hidden states, and a fully connected layer on to to output the prediction.
class MyRnn(nn.Module):
def __init__(self, in_d=2, out_d=2, hidden_d=8, num_hidden=1):
super(MyRnn, self).__init__()
self.rnn = nn.RNN(input_size=in_d, hidden_size=hidden_d, num_layers=num_hidden)
self.fc = nn.Linear(hidden_d, out_d)
def forward(self, x, h0):
r, h = self.rnn(x, h0)
y = self.fc(r) # no activation on the output
return y, h
You can use your two sequences as training data, each sequence is a tensor of shape Tx1x2 where T is the sequence length, and each entry is two dimensional (x-y).
To predict (during training):
rnn = MyRnn()
pred, out_h = rnn(seq[:-1, ...], torch.zeros(1, 1, 8)) # given time t predict t+1
err = criterion(pred, seq[1:, ...]) # compare prediction to t+1
Once the model is trained, you can show it first k steps and continue to predict the next steps:
rnn.eval()
with torch.no_grad():
pred, h = rnn(s[:k,...], torch.zeros(1, 1, 8, dtype=torch.float))
# pred[-1, ...] is the predicted next step
prev = pred[-1:, ...]
for j in range(k+1, s.shape[0]):
pred, h = rnn(prev, h) # note how we keep track of the hidden state of the model. it is no longer init to zero.
prev = pred
I put everything together in a colab notebook so you can play with it.
For simplicity, I ignored the data normalization here, but you can find it in the colab notebook.
What's next?
These types of predictions are prone to error accumulation. This should be addressed during training, by shifting the inputs from the ground truth "clean" sequences to the actual predicted sequences, so the model will be able to compensate for its errors.
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).
I would like to code with Keras a neural network that acts both as an autoencoder AND a classifier for semi-supervised learning. Take for example this dataset where there is a few labeled images and a lot of unlabeled images: https://cs.stanford.edu/~acoates/stl10/
Some papers listed here achieved that, or very similar things, successfully.
To sum up: if the model would have the same input data shape and the same "encoding" convolutional layers, but would split into two heads (fork-style), so there is a classification head and a decoding head, in a way that the unsupervised autoencoder will contribute to a good learning for the classification head.
With TensorFlow there would be no problem doing that as we have full control over the computational graph.
But with Keras, things are more high-level and I feel that all the calls to ".fit" must always provide all the data at once (so it would force me to tie together the classification head and the autoencoding head into one time-step).
One way in keras to almost do that would be with something that goes like this:
input = Input(shape=(32, 32, 3))
cnn_feature_map = sequential_cnn_trunk(input)
classification_predictions = Dense(10, activation='sigmoid')(cnn_feature_map)
autoencoded_predictions = decode_cnn_head_sequential(cnn_feature_map)
model = Model(inputs=[input], outputs=[classification_predictions, ])
model.compile(optimizer='rmsprop',
loss='binary_crossentropy',
metrics=['accuracy'])
model.fit([images], [labels, images], epochs=10)
However, I think and I fear that if I just want to fit things in that way it will fail and ask for the missing head:
for epoch in range(10):
# classifications step
model.fit([images], [labels, None], epochs=1)
# "semi-unsupervised" autoencoding step
model.fit([images], [None, images], epochs=1)
# note: ".train_on_batch" could probably be used rather than ".fit" to avoid doing a whole epoch each time.
How should one implement that behavior with Keras? And could the training be done jointly without having to split the two calls to the ".fit" function?
Sometimes when you don't have a label you can pass zero vector instead of one hot encoded vector. It should not change your result because zero vector doesn't have any error signal with categorical cross entropy loss.
My custom to_categorical function looks like this:
def tricky_to_categorical(y, translator_dict):
encoded = np.zeros((y.shape[0], len(translator_dict)))
for i in range(y.shape[0]):
if y[i] in translator_dict:
encoded[i][translator_dict[y[i]]] = 1
return encoded
When y contains labels, and translator_dict is a python dictionary witch contains labels and its unique keys like this:
{'unisex':2, 'female': 1, 'male': 0}
If an UNK label can't be found in this dictinary then its encoded label will be a zero vector
If you use this trick you also have to modify your accuracy function to see real accuracy numbers. you have to filter out all zero vectors from our metrics
def tricky_accuracy(y_true, y_pred):
mask = K.not_equal(K.sum(y_true, axis=-1), K.constant(0)) # zero vector mask
y_true = tf.boolean_mask(y_true, mask)
y_pred = tf.boolean_mask(y_pred, mask)
return K.cast(K.equal(K.argmax(y_true, axis=-1), K.argmax(y_pred, axis=-1)), K.floatx())
note: You have to use larger batches (e.g. 32) in order to prevent zero matrix update, because It can make your accuracy metrics crazy, I don't know why
Alternative solution
Use Pseudo Labeling :)
you can train jointly, you have to pass an array insted of single label.
I used fit_generator, e.g.
model.fit_generator(
batch_generator(),
steps_per_epoch=len(dataset) / batch_size,
epochs=epochs)
def batch_generator():
batch_x = np.empty((batch_size, img_height, img_width, 3))
gender_label_batch = np.empty((batch_size, len(gender_dict)))
category_label_batch = np.empty((batch_size, len(category_dict)))
while True:
i = 0
for idx in np.random.choice(len(dataset), batch_size):
image_id = dataset[idx][0]
batch_x[i] = load_and_convert_image(image_id)
gender_label_batch[i] = gender_labels[idx]
category_label_batch[i] = category_labels[idx]
i += 1
yield batch_x, [gender_label_batch, category_label_batch]
I am attempting to train an ANN on time series data in Keras. I have three vectors of data that are broken into scrolling window sequences (i.e. for vector l).
np.array([l[i:i+window_size] for i in range( len(l) - window_size)])
The target vector is similarly windowed so the neural net output is a prediction of the target vector for the next window_size number of time steps. All the data is normalized with a min-max scaler. It is fed into the neural network as a shape=(nb_samples, window_size, 3). Here is a plot of the 3 input vectors.
The only output I've managed to muster from the ANN is the following plot. Target vector in blue, predictions in red (plot is zoomed in to make the prediction pattern legible). Prediction vectors are plotted at window_size intervals so each one of the repeated patterns is one prediction from the net.
I've tried many different model architectures, number of epochs, activation functions, short and fat networks, skinny, tall. This is my current one (it's a little out there).
Conv1D(64,4, input_shape=(None,3)) ->
Conv1d(32,4) ->
Dropout(24) ->
LSTM(32) ->
Dense(window_size)
But nothing I try will affect the neural net from outputting this repeated pattern. I must be misunderstanding something about time-series or LSTMs in Keras. But I'm very lost at this point so any help is greatly appreciated. I've attached the full code at this repository.
https://github.com/jaybutera/dat-toy
I played with your code a little and I think I have a few suggestions for getting you on the right track. The code doesn't seem to match your graphs exactly, but I assume you've tweaked it a bit since then. Anyway, there are two main problems:
The biggest problem is in your data preparation step. You basically have the data shapes backwards, in that you have a single timestep of input for X and a timeseries for Y. Your input shape is (18830, 1, 8), when what you really want is (18830, 30, 8) so that the full 30 timesteps are fed into the LSTM. Otherwise the LSTM is only operating on one timestep and isn't really useful. To fix this, I changed the line in common.py from
X = X.reshape(X.shape[0], 1, X.shape[1])
to
X = windowfy(X, winsize)
Similarly, the output data should probably be only 1 value, from what I've gathered of your goals from the plotting function. There are certainly some situations where you want to predict a whole timeseries, but I don't know if that's what you want in this case. I changed Y_train to use fuels instead of fuels_w so that it only had to predict one step of the timeseries.
Training for 100 epochs might be way too much for this simple network architecture. In some cases when I ran it, it looked like there was some overfitting going on. Observing the decrease of loss in the network, it seems like maybe only 3-4 epochs are needed.
Here is the graph of predictions after 3 training epochs with the adjustments I mentioned. It's not a great prediction, but it looks like it's on the right track now at least. Good luck to you!
EDIT: Example predicting multiple output timesteps:
from sklearn import datasets, preprocessing
import numpy as np
from scipy import stats
from keras import models, layers
INPUT_WINDOW = 10
OUTPUT_WINDOW = 5 # Predict 5 steps of the output variable.
# Randomly generate some regression data (not true sequential data; samples are independent).
np.random.seed(11798)
X, y = datasets.make_regression(n_samples=1000, n_features=4, noise=.1)
# Rescale 0-1 and convert into windowed sequences.
X = preprocessing.MinMaxScaler().fit_transform(X)
y = preprocessing.MinMaxScaler().fit_transform(y.reshape(-1, 1))
X = np.array([X[i:i + INPUT_WINDOW] for i in range(len(X) - INPUT_WINDOW)])
y = np.array([y[i:i + OUTPUT_WINDOW] for i in range(INPUT_WINDOW - OUTPUT_WINDOW,
len(y) - OUTPUT_WINDOW)])
print(np.shape(X)) # (990, 10, 4) - Ten timesteps of four features
print(np.shape(y)) # (990, 5, 1) - Five timesteps of one features
# Construct a simple model predicting output sequences.
m = models.Sequential()
m.add(layers.LSTM(20, activation='relu', return_sequences=True, input_shape=(INPUT_WINDOW, 4)))
m.add(layers.LSTM(20, activation='relu'))
m.add(layers.RepeatVector(OUTPUT_WINDOW))
m.add(layers.LSTM(20, activation='relu', return_sequences=True))
m.add(layers.wrappers.TimeDistributed(layers.Dense(1, activation='sigmoid')))
print(m.summary())
m.compile(optimizer='adam', loss='mse')
m.fit(X[:800], y[:800], batch_size=10, epochs=60) # Train on first 800 sequences.
preds = m.predict(X[800:], batch_size=10) # Predict the remaining sequences.
print('Prediction:\n' + str(preds[0]))
print('Actual:\n' + str(y[800]))
# Correlation should be around r = .98, essentially perfect.
print('Correlation: ' + str(stats.pearsonr(y[800:].flatten(), preds.flatten())[0]))