The goal is to predict a timeseries Y of 87601 timesteps (10 years) and 9 targets. The input features X (exogenous input) are 11 timeseries of 87600 timesteps. The output has one more timestep, as this is the initial value.
The output Yt at timestep t depends on the input Xt and on the previous output Yt-1.
Hence, the model should look like this: Model layout
I could only find this thread on this: LSTM: How to feed the output back to the input? #4068.
I tried to implemented this with Keras as follows:
def build_model():
# Input layers
input_x = layers.Input(shape=(features,), name='input_x')
input_y = layers.Input(shape=(targets,), name='input_y-1')
# Merge two inputs
merge = layers.concatenate([input_x,input_y], name='merge')
# Normalise input
norm = layers.Lambda(normalise, name='scale')(merge)
# Hidden layers
x = layers.Dense(128, input_shape=(features,))(norm)
# Output layer
output = layers.Dense(targets, activation='relu', name='output')(x)
model = Model(inputs=[input_x,input_y], outputs=output)
model.compile(loss='mean_squared_error', optimizer=Adam())
return model
def make_prediction(model, X, y):
y_pred = [y[0,None,:]]
for i in range(len(X)):
y_pred.append(model.predict([X[i,None,:],y_pred[i]]))
y_pred = np.asarray(y_pred)
y_pred = y_pred.reshape(y_pred.shape[0],y_pred.shape[2])
return y_pred
# Fit
model = build_model()
model.fit([X_train, y_train[:-1]], [y_train[1:]]], epochs=200,
batch_size=24, shuffle=False)
# Predict
y_hat = make_prediction(model, X_train, y_train)
This works, but is it not what I want to achieve, as there is no connection between input and output. Hence, the model doesn't learn how to correct for an error in the fed-back output, which results in poor accuracy when predicting as the error on the output is accumulated at every timestep.
Is there a way in Keras to implement the output-input feed-back during training stage?
Also, as the initial value of Y is always known, I want to feed this to the network as well.
Related
I am getting acquainted with Tensorflow-Probability and here I am running into a problem. During training, the model returns nan as the loss (possibly meaning a huge loss that causes overflowing). Since the functional form of the synthetic data is not overly complicated and the ratio of data points to parameters is not frightening at first glance at least I wonder what is the problem and how it could be corrected.
The code is the following --accompanied by some possibly helpful images:
# Create and plot 5000 data points
x_train = np.linspace(-1, 2, 5000)[:, np.newaxis]
y_train = np.power(x_train, 3) + 0.1*(2+x_train)*np.random.randn(5000)[:, np.newaxis]
plt.scatter(x_train, y_train, alpha=0.1)
plt.show()
# Define the prior weight distribution -- all N(0, 1) -- and not trainable
def prior(kernel_size, bias_size, dtype = None):
n = kernel_size + bias_size
prior_model = Sequential([
tfpl.DistributionLambda(
lambda t: tfd.MultivariateNormalDiag(loc = tf.zeros(n) , scale_diag = tf.ones(n)
))
])
return(prior_model)
# Define variational posterior weight distribution -- multivariate Gaussian
def posterior(kernel_size, bias_size, dtype = None):
n = kernel_size + bias_size
posterior_model = Sequential([
tfpl.VariableLayer(tfpl.MultivariateNormalTriL.params_size(n) , dtype = dtype), # The parameters of the model are declared Variables that are trainable
tfpl.MultivariateNormalTriL(n) # The posterior function will return to the Variational layer that will call it a MultivariateNormalTril object that will have as many dimensions
# as the parameters of the Variational Dense Layer. That means that each parameter will be generated by a distinct Normal Gaussian shifted and scaled
# by a mu and sigma learned from the data, independently of all the other weights. The output of this Variablelayer will become the input to the
# MultivariateNormalTriL object.
# The shape of the VariableLayer object will be defined by the number of paramaters needed to create the MultivariateNormalTriL object given
# that it will live in a Space of n dimensions (event_size = n). This number is returned by the tfpl.MultivariateNormalTriL.params_size(n)
])
return(posterior_model)
x_in = Input(shape = (1,))
x = tfpl.DenseVariational(units= 2**4,
make_prior_fn=prior,
make_posterior_fn=posterior,
kl_weight=1/x_train.shape[0],
activation='relu')(x_in)
x = tfpl.DenseVariational(units= 2**4,
make_prior_fn=prior,
make_posterior_fn=posterior,
kl_weight=1/x_train.shape[0],
activation='relu')(x)
x = tfpl.DenseVariational(units=tfpl.IndependentNormal.params_size(1),
make_prior_fn=prior,
make_posterior_fn=posterior,
kl_weight=1/x_train.shape[0])(x)
y_out = tfpl.IndependentNormal(1)(x)
model = Model(inputs = x_in, outputs = y_out)
def nll(y_true, y_pred):
return -y_pred.log_prob(y_true)
model.compile(loss=nll, optimizer= 'Adam')
model.summary()
Train the model
history = model.fit(x_train1, y_train1, epochs=500)
The problem seems to be in the loss function: negative log-likelihood of the independent normal distribution without any specified location and scale leads to the untamed variance which leads to the blowing up the final loss value. Since you're experimenting with the variational layers, you must be interested in the estimation of the epistemic uncertainty, to that end, I'd recommend to apply the constant variance.
I tried to make a couple of slight changes to your code within the following lines:
first of all, the final output y_out comes directly from the final variational layer without any IndpendnetNormal distribution layer:
y_out = tfpl.DenseVariational(units=1,
make_prior_fn=prior,
make_posterior_fn=posterior,
kl_weight=1/x_train.shape[0])(x)
second, the loss function now contains the necessary calculations with the normal distribution you need but with the static variance in order to avoid the blowing up of the loss during training:
def nll(y_true, y_pred):
dist = tfp.distributions.Normal(loc=y_pred, scale=1.0)
return tf.reduce_sum(-dist.log_prob(y_true))
then the model is compiled and trained in the same way as before:
model.compile(loss=nll, optimizer= 'Adam')
history = model.fit(x_train, y_train, epochs=3000)
and finally let's sample 100 different predictions from the trained model and plot these values to visualize the epistemic uncertainty of the model:
predicted = [model(x_train) for _ in range(100)]
for i, res in enumerate(predicted):
plt.plot(x_train, res , alpha=0.1)
plt.scatter(x_train, y_train, alpha=0.1)
plt.show()
After 3000 epochs the result looks like this (with the reduced number of training points to 3000 instead of 5000 to speed-up the training):
The model has 38,589 trainable parameters but you have only 5,000 points as data; so, effective training is impossible with so many parameters.
I Make a sentiment analysis model using LSTM but my model gives very bad prediction.
Here is the complete code
Dataset for amazon review
My LSTM model looks like this:
def ltsm_model(input_shape, word_to_vec_map, word_to_index):
"""
Function creating the ltsm_model model's graph.
Arguments:
input_shape -- shape of the input, usually (max_len,)
word_to_vec_map -- dictionary mapping every word in a vocabulary into its 50-dimensional vector representation
word_to_index -- dictionary mapping from words to their indices in the vocabulary (400,001 words)
Returns:
model -- a model instance in Keras
"""
### START CODE HERE ###
# Define sentence_indices as the input of the graph, it should be of shape input_shape and dtype 'int32' (as it contains indices).
sentence_indices = Input(shape=input_shape, dtype='int32')
# Create the embedding layer pretrained with GloVe Vectors (≈1 line)
embedding_layer = pretrained_embedding_layer(word_to_vec_map, word_to_index)
# Propagate sentence_indices through your embedding layer, you get back the embeddings
embeddings = embedding_layer(sentence_indices)
# Propagate the embeddings through an LSTM layer with 128-dimensional hidden state
# Be careful, the returned output should be a batch of sequences.
X = LSTM(128, return_sequences=True)(embeddings)
# Add dropout with a probability of 0.5
X = Dropout(0.5)(X)
# Propagate X trough another LSTM layer with 128-dimensional hidden state
# Be careful, the returned output should be a single hidden state, not a batch of sequences.
X = LSTM(128, return_sequences=False)(X)
# Add dropout with a probability of 0.5
X = Dropout(0.5)(X)
# Propagate X through a Dense layer with softmax activation to get back a batch of 5-dimensional vectors.
X = Dense(2, activation='relu')(X)
# Add a softmax activation
X = Activation('softmax')(X)
# Create Model instance which converts sentence_indices into X.
model = Model(inputs=[sentence_indices], outputs=X)
### END CODE HERE ###
return model
Here is what my training dataset looks like:
This is my testing data:
x_test = np.array(['amazing!: this soundtrack is my favorite music..'])
X_test_indices = sentences_to_indices(x_test, word_to_index, maxLen)
print(x_test[0] +' '+ str(np.argmax(model.predict(X_test_indices))))
I got following out for this:
amazing!: this soundtrack is my favorite music.. 0
But it should be positive sentiment and should be 1
Also this my fit model output:
How can I improve my model performance? This pretty bad model I suppose.
I am using the input gradient as feature important and want to compare the feature importance of a train datapoint with the human annotated feature importance. I would like to make this comparison differentiable such that it can be learned through backpropagation. For that, I am writing a custom loss function that in addition to the regular loss (e.g. m.s.e. on the prediction vs true labels) also checks whether the input gradient is correct (e.g. m.s.e. of the input gradient vs the human annotated feature importance).
With the following code I am able to get the input gradient:
from keras import backend as K
import numpy as np
from keras.models import Model
from keras.layers import Input, Dense
def normalize(x):
# utility function to normalize a tensor by its L2 norm
return x / (K.sqrt(K.mean(K.square(x))) + 1e-5)
# Amount of training samples
N = 1000
input_dim = 10
# Generate training set make the 1st and 2nd feature same as the target feature
X = np.random.standard_normal(size=(N, input_dim))
y = np.random.randint(low=0, high=2, size=(N, 1))
X[:, 1] = y[:, 0]
X[:, 2] = y[:, 0]
# Create simple model
inputs = Input(shape=(input_dim,))
x = Dense(10, name="dense1")(inputs)
output = Dense(1, activation='sigmoid')(x)
model = Model(input=[inputs], output=output)
# Compile and fit model
model.compile(optimizer='adam', loss="mse", metrics=['accuracy'])
model.fit([X], y, epochs=100, batch_size=64)
# Get function to get input gradients
gradients = K.gradients(model.output, model.input)[0]
gradient_function = K.function([model.input], [normalize(gradients)])
# Get input gradient values of the training-set
grads_val = gradient_function([X])[0]
print(grads_val[:2])
This prints the following (you can see that the 1st and the 2nd features have the highest importance):
[[ 1.2629046e-02 2.2765596e+00 2.1479919e+00 2.1558853e-02
4.5277486e-03 2.9851785e-03 9.5279224e-04 -1.0903150e-02
-1.2230731e-02 2.1960819e-02]
[ 1.1318034e-02 2.0402350e+00 1.9250139e+00 1.9320872e-02
4.0577268e-03 2.6752844e-03 8.5390132e-04 -9.7713526e-03
-1.0961102e-02 1.9681118e-02]]
How can I write a custom loss function in which the input gradients are differentiable?
I started with the following loss function.
from keras.losses import mean_squared_error
def custom_loss():
# human annotated feature importance
# Let's say that it says to only look at the second feature
human_feature_importance = []
for i in range(N):
human_feature_importance.append([0,0,1,0,0,0,0,0,0,0])
def loss(y_true, y_pred):
# Get regular loss
regular_loss_value = mean_squared_error(y_true, y_pred)
# Somehow get the input gradient of each training sample as a tensor
# It should be differential w.r.t. all of the weights
gradients = ??
feature_importance_loss_value = mean_squared_error(gradients, human_feature_importance)
# Combine the both losses
return regular_loss_value + feature_importance_loss_value
return loss
I also found an implementation in tensorflow to make the input gradient differentialble: https://github.com/dtak/rrr/blob/master/rrr/tensorflow_perceptron.py#L18
I am trying to train a recurrent model in Keras containing an LSTM for regression purposes.
I would like to use the model online and, as far as I understood, I need to train a stateful LSTM.
Since the model has to output a sequence of values, I hope it computes the loss on each of the expected output vector.
However, I fear my code is not working this way and I would be grateful if anyone would help me to understand if I am doing right or if there is some better approach.
The input to the model is a sequence of 128-dimensional vectors. Each sequence in the training set has a different lenght.
At each time, the model should output a vector of 3 elements.
I am trying to train and compare two models:
A) a simple LSTM with 128 inputs and 3 outputs;
B) a simple LSTM with 128 inputs and 100 outputs + a dense layer with 3 outputs;
For model A) I wrote the following code:
# Model
model = Sequential()
model.add(LSTM(3, batch_input_shape=(1, None, 128), return_sequences=True, activation = "linear", stateful = True))`
model.compile(loss='mean_squared_error', optimizer=Adam())
# Training
for i in range(n_epoch):
for j in np.random.permutation(n_sequences):
X = data[j] # j-th sequences
X = X[np.newaxis, ...] # X has size 1 x NTimes x 128
Y = dataY[j] # Y has size NTimes x 3
history = model.fit(X, Y, epochs=1, batch_size=1, verbose=0, shuffle=False)
model.reset_states()
With this code, model A) seems to train fine because the output sequence approaches the ground-truth sequence on the training set.
However, I wonder if the loss is really computed by considering all NTimes output vectors.
For model B), I could not find any way to get the entire output sequence due to the dense layer. Hence, I wrote:
# Model
model = Sequential()
model.add(LSTM(100, batch_input_shape=(1, None, 128), , stateful = True))
model.add(Dense(3, activation="linear"))
model.compile(loss='mean_squared_error', optimizer=Adam())
# Training
for i in range(n_epoch):
for j in np.random.permutation(n_sequences):
X = data[j] #j-th sequence
X = X[np.newaxis, ...] # X has size 1 x NTimes x 128
Y = dataY[j] # Y has size NTimes x 3
for h in range(X.shape[1]):
x = X[0,h,:]
x = x[np.newaxis, np.newaxis, ...] # h-th vector in j-th sequence
y = Y[h,:]
y = y[np.newaxis, ...]
loss += model.train_on_batch(x,y)
model.reset_states() #After the end of the sequence
With this code, model B) does not train fine. It seems to me the training does not converge and loss values increase and decrease cyclically
I have also tried to use as Y only the last vector and them calling the fit function on the Whole training sequence X, but no improvements.
Any idea? Thank you!
If you want to still have three outputs per step of your sequence, you need to TimeDistribute your Dense layer like so:
model.add(TimeDistributed(Dense(3, activation="linear")))
This applies the dense layer to each timestep independently.
See https://keras.io/layers/wrappers/#timedistributed
I have a network in Keras with many outputs, however, my training data only provides information for a single output at a time.
At the moment my method for training has been to run a prediction on the input in question, change the value of the particular output that I am training and then doing a single batch update. If I'm right this is the same as setting the loss for all outputs to zero except the one that I'm trying to train.
Is there a better way? I've tried class weights where I set a zero weight for all but the output I'm training but it doesn't give me the results I expect?
I'm using the Theano backend.
Outputting multiple results and optimizing only one of them
Let's say you want to return output from multiple layers, maybe from some intermediate layers, but you need to optimize only one target output. Here's how you can do it:
Let's start with this model:
inputs = Input(shape=(784,))
x = Dense(64, activation='relu')(inputs)
# you want to extract these values
useful_info = Dense(32, activation='relu', name='useful_info')(x)
# final output. used for loss calculation and optimization
result = Dense(1, activation='softmax', name='result')(useful_info)
Compile with multiple outputs, set loss as None for extra outputs:
Give None for outputs that you don't want to use for loss calculation and optimization
model = Model(inputs=inputs, outputs=[result, useful_info])
model.compile(optimizer='rmsprop',
loss=['categorical_crossentropy', None],
metrics=['accuracy'])
Provide only target outputs when training. Skipping extra outputs:
model.fit(my_inputs, {'result': train_labels}, epochs=.., batch_size=...)
# this also works:
#model.fit(my_inputs, [train_labels], epochs=.., batch_size=...)
One predict to get them all
Having one model you can run predict only once to get all outputs you need:
predicted_labels, useful_info = model.predict(new_x)
In order to achieve this I ended up using the 'Functional API'. You basically create multiple models, using the same layers input and hidden layers but different output layers.
For example:
https://keras.io/getting-started/functional-api-guide/
from keras.layers import Input, Dense
from keras.models import Model
# This returns a tensor
inputs = Input(shape=(784,))
# a layer instance is callable on a tensor, and returns a tensor
x = Dense(64, activation='relu')(inputs)
x = Dense(64, activation='relu')(x)
predictions_A = Dense(1, activation='softmax')(x)
predictions_B = Dense(1, activation='softmax')(x)
# This creates a model that includes
# the Input layer and three Dense layers
modelA = Model(inputs=inputs, outputs=predictions_A)
modelA.compile(optimizer='rmsprop',
loss='categorical_crossentropy',
metrics=['accuracy'])
modelB = Model(inputs=inputs, outputs=predictions_B)
modelB.compile(optimizer='rmsprop',
loss='categorical_crossentropy',
metrics=['accuracy'])