I have 2000 labelled data (7 different labels) and about 100K unlabeled data and I am trying to use sklearn.semi_supervised.LabelPropagation. The data has 1024 dimensions. My problem is that the classifier is labeling everything as 1. My code looks like this:
X_unlabeled = X_unlabeled[:10000, :]
X_both = np.vstack((X_train, X_unlabeled))
y_both = np.append(y_train, -np.ones((X_unlabeled.shape[0],)))
clf = LabelPropagation(max_iter=100).fit(X_both, y_both)
y_pred = clf.predict(X_test)
y_pred is all ones. Also, X_train is 2000x1024 and X_unlabeled is a subset of the unlabeled data which is 10000x1024.
I also get this error upon calling fit on the classifier:
/usr/local/lib/python2.7/site-packages/sklearn/semi_supervised/label_propagation.py:255: RuntimeWarning: invalid value encountered in divide
self.label_distributions_ /= normalizer
Have you tried different values for the gamma parameter ? As the graph is constructed by computing an rbf kernel, the computation includes an exponential and the python exponential functions return 0 if the value is a too big negative number (see http://computer-programming-forum.com/56-python/ef71e144330ffbc2.htm). And if the graph is filled with 0, the label_distributions_ is filled with "nan" (because of normalization) and a warning appears. (be careful, the gamma value in scikit implementation is multiplied to the euclidean distance, it's not the same thing as in the Zhu paper.)
The LabelPropagation will finally be fixed in version 0.19
Related
I am new babie to the Deep Learning field, and I am use log-likelihood method to compare the MSE metrics.Could anyone be able to show how to calculate the following 2 predicted output examples with 3 outputs neurons each. Thanks
yt = [ [1,0,0],[0,0,1]]
yp = [ [0.9, 0.2,0.2], [0.2,0.8,0.3] ]
MSE or Mean Squared Error is simply the expected value of the squared difference between the predicted and the ground truth labels, represented as
\text{MSE}(\hat{\theta}) = E\left[(\hat{\theta} - \theta)^2\right]
where theta is the ground truth labels and theta^hat is the predicted labels
I am not sure what are you referring to exactly, like a theoretical question or a part of code
As a Python implementation
def mean_squared_error(A, B):
return np.square(np.subtract(A,B)).mean()
yt = [[1,0,0],[0,0,1]]
yp = [[0.9, 0.2,0.2], [0.2,0.8,0.3]]
mse = mean_squared_error(yt, yp)
print(mse)
This will give a value of 0.21
If you are using one of the DL frameworks like TensorFlow, then they are already providing the function which calculates the mse loss between tensors
tf.losses.mean_squared_error
where
tf.losses.mean_squared_error(
labels,
predictions,
weights=1.0,
scope=None,
loss_collection=tf.GraphKeys.LOSSES,
reduction=Reduction.SUM_BY_NONZERO_WEIGHTS
)
Args:
labels: The ground truth output tensor, same dimensions as 'predictions'.
predictions: The predicted outputs.
weights: Optional Tensor whose rank is either 0, or the same rank as labels, and must be broadcastable to labels (i.e., all dimensions
must be either 1, or the same as the corresponding losses dimension).
scope: The scope for the operations performed in computing the loss.
loss_collection: collection to which the loss will be added.
reduction: Type of reduction to apply to loss.
Returns:
Weighted loss float Tensor. If reduction is NONE, this has the same
shape as labels; otherwise, it is scalar.
I have a multilabel classification problem, I used the following code but the validation accuracy jumps to 99% in the first epoch which is weird given the complexity of the data as the input features are 2048 extracted from inception model (pool3:0) layer and the labels are [1000],(here is the link of a file contains samples of features and label : https://drive.google.com/file/d/0BxI_8PO3YBPPYkp6dHlGeExpS1k/view?usp=sharing ),
is there something I am doing wrong here ??
Note: labels are sparse vector contain only 1 ~ 10 entry as 1 the rest is zeros
model.compile(optimizer='adadelta', loss='binary_crossentropy', metrics=['accuracy'])
The output of prediction is zeros !
What wrong I do in training the model to bother the prediction ?
#input is the features file and labels file
def generate_arrays_from_file(path ,batch_size=100):
x=np.empty([batch_size,2048])
y=np.empty([batch_size,1000])
while True:
f = open(path)
i = 1
for line in f:
# create Numpy arrays of input data
# and labels, from each line in the file
words=line.split(',')
words=map(float, words[1:])
x_= np.array(words[0:2048])
y_=words[2048:]
y_= np.array(map(int,y_))
x_=x_.reshape((1, -1))
#print np.squeeze(x_)
y_=y_.reshape((1,-1))
x[i]= x_
y[i]=y_
i += 1
if i == batch_size:
i=1
yield (x, y)
f.close()
model = Sequential()
model.add(Dense(units=2048, activation='sigmoid', input_dim=2048))
model.add(Dense(units=1000, activation="sigmoid",
kernel_initializer="uniform"))
model.compile(optimizer='adadelta', loss='binary_crossentropy', metrics=
['accuracy'])
model.fit_generator(generate_arrays_from_file('train.txt'),
validation_data= generate_arrays_from_file('test.txt'),
validation_steps=1000,epochs=100,steps_per_epoch=1000,
verbose=1)
I think the problem with the accuracy is that your output are sparse.
Keras computes accuracy using this formula:
K.mean(K.equal(y_true, K.round(y_pred)), axis=-1)
So, in your case, having only 1~10 non zero labels, a prediction of all 0 will yield an accuracy of 99.9% ~ 99%.
As far as the problem not learning, I think the problem is that you are using a sigmoid as last activation and using 0 or 1 as output value. This is bad practice since, in order for the sigmoid to return 0 or 1 the values it gets as input must be very large or very small, which reflects on the net having very large (in absolute value) weights. Furthermore, since in each training output there are far less 1 than 0 the network will soon get to a stationary point in which it simply outputs all zeros (the loss in this case is not very large either, should be around 0.016~0.16).
What you can do is scale your output labels so that they are between (0.2, 0.8) for example so that the weights of the net won't become too big or too small. Alternatively you can use a relu as activation function.
Did you try to use the cosine similarity as loss function?
I had the same multi-label + high dimensionality problem.
The cosine distance takes account of the orientation of the model output (prediction) and the desired output (true class) vector.
It is the normalized dot-product between two vectors.
In keras the cosine_proximity function is -1*cosine_distance. Meaning that -1 corresponds to two vectors with the same size and orientation.
Assuming after performing median frequency balancing for images used for segmentation, we have these class weights:
class_weights = {0: 0.2595,
1: 0.1826,
2: 4.5640,
3: 0.1417,
4: 0.9051,
5: 0.3826,
6: 9.6446,
7: 1.8418,
8: 0.6823,
9: 6.2478,
10: 7.3614,
11: 0.0}
The idea is to create a weight_mask such that it could be multiplied by the cross entropy output of both classes. To create this weight mask, we can broadcast the values based on the ground_truth labels or the predictions. Some mathematics in my implementation:
Both labels and logits are of shape [batch_size, height, width, num_classes]
The weight mask is of shape [batch_size, height, width, 1]
The weight mask is broadcasted to the num_classes number of channels of the multiplication between the softmax of the logit and the labels to give an output shape of [batch_size, height, width, num_classes]. In this case, num_classes is 12.
Reduce sum for each example in a batch, then perform reduce mean for all examples in one batch to get a single scalar value of loss.
In this case, should we create the weight mask based on the predictions or the ground truth?
If we build it based on the ground_truth, then it means no matter what the predicted pixel labels are, they get penalized based on the actual labels of the class, which doesn't seem to guide the training in a sensible way.
But if we build it based on the predictions, then for whatever logit predictions that are produced, if the predicted label (from taking the argmax of the logit) is dominant, then the logit values for that pixel will all be reduced by a significant amount.
--> Although this means the maximum logit will still be the maximum since all of the logits in the 12 channels will be scaled by the same value, the final softmax probability of the label predicted (which is still the same before and after scaling), will be lower than before scaling (did some simple math to estimate). --> a lower loss is predicted
But the problem is this: If a lower loss is predicted as a result of this weighting, then wouldn't it contradict the idea that predicting dominant labels should give you a greater loss?
The impression I get in total for this method is that:
For the dominant labels, they are penalized and rewarded much lesser.
For the less dominant labels, they are rewarded highly if the predictions are correct, but they're also penalized heavily for a wrong prediction.
So how does this help to tackle the issue of class-balancing? I don't quite get the logic here.
IMPLEMENTATION
Here is my current implementation for calculating the weighted cross entropy loss, although I'm not sure if it is correct.
def weighted_cross_entropy(logits, onehot_labels, class_weights):
if not logits.dtype == tf.float32:
logits = tf.cast(logits, tf.float32)
if not onehot_labels.dtype == tf.float32:
onehot_labels = tf.cast(onehot_labels, tf.float32)
#Obtain the logit label predictions and form a skeleton weight mask with the same shape as it
logit_predictions = tf.argmax(logits, -1)
weight_mask = tf.zeros_like(logit_predictions, dtype=tf.float32)
#Obtain the number of class weights to add to the weight mask
num_classes = logits.get_shape().as_list()[3]
#Form the weight mask mapping for each pixel prediction
for i in xrange(num_classes):
binary_mask = tf.equal(logit_predictions, i) #Get only the positions for class i predicted in the logits prediction
binary_mask = tf.cast(binary_mask, tf.float32) #Convert boolean to ones and zeros
class_mask = tf.multiply(binary_mask, class_weights[i]) #Multiply only the ones in the binary mask with the specific class_weight
weight_mask = tf.add(weight_mask, class_mask) #Add to the weight mask
#Multiply the logits with the scaling based on the weight mask then perform cross entropy
weight_mask = tf.expand_dims(weight_mask, 3) #Expand the fourth dimension to 1 for broadcasting
logits_scaled = tf.multiply(logits, weight_mask)
return tf.losses.softmax_cross_entropy(onehot_labels=onehot_labels, logits=logits_scaled)
Could anyone verify whether my concept of this weighted loss is correct, and whether my implementation is correct? This is my first time getting acquainted with a dataset with imbalanced class, and so I would really appreciate it if anyone could verify this.
TESTING RESULTS: After doing some tests, I found the implementation above results in a greater loss. Is this supposed to be the case? i.e. Would this make the training harder but produce a more accurate model eventually?
SIMILAR THREADS
Note that I have checked a similar thread here: How can I implement a weighted cross entropy loss in tensorflow using sparse_softmax_cross_entropy_with_logits
But it seems that TF only has a sample-wise weighting for loss but not a class-wise one.
Many thanks to all of you.
Here is my own implementation in Keras using the TensorFlow backend:
def class_weighted_pixelwise_crossentropy(target, output):
output = tf.clip_by_value(output, 10e-8, 1.-10e-8)
with open('class_weights.pickle', 'rb') as f:
weight = pickle.load(f)
return -tf.reduce_sum(target * weight * tf.log(output))
where weight is just a standard Python list with the indexes of the weights matched to those of the corresponding class in the one-hot vectors. I store the weights as a pickle file to avoid having to recalculate them. It is an adaptation of the Keras categorical_crossentropy loss function. The first line simply clips the value to make sure we never take the log of 0.
I am unsure why one would calculate the weights using the predictions rather than the ground truth; if you provide further explanation I can update my answer in response.
Edit: Play around with this numpy code to understand how this works. Also review the definition of cross entropy.
import numpy as np
weights = [1,2]
target = np.array([ [[0.0,1.0],[1.0,0.0]],
[[0.0,1.0],[1.0,0.0]]])
output = np.array([ [[0.5,0.5],[0.9,0.1]],
[[0.9,0.1],[0.4,0.6]]])
crossentropy_matrix = -np.sum(target * np.log(output), axis=-1)
crossentropy = -np.sum(target * np.log(output))
The output for network which recognizes MNIST database is predictions for 10 classes, i.e. for 1000 images we will have matrix of size (1000, 10). Which way represents cost function better (and why?):
simple tf.squared_difference(Y_pred, Y_pred)?
mean over batches tf.reduce_mean(tf.tf.squared_difference(Y_pred, Y_pred), axis=0)
or mean over classes and then over batches tf.reduce_men(tf.reduce_mean(tf.tf.squared_difference(Y_pred, Y_pred), axis=1))
Thanks
Since your targets are categories (numbers from 0 to 9), it is better to use a cross entropy cost function, and do something like that:
cross_entropy = -tf.reduce_sum(Y * tf.log(Y_pred + 1e-10))
optimizer = tf.train.AdamOptimizer(0.001).minimize(cross_entropy)
Here Y are the real target values, and Y_pred are the predicted target values.
Here is a discussion of the benefits of cross entropy over mean square error for classification problems.
I am training a neural network for multilabel classification, with a large number of classes (1000). Which means more than one output can be active for every input. On an average, I have two classes active per output frame. On training with a cross entropy loss the neural network resorts to outputting only zeros, because it gets the least loss with this output since 99.8% of my labels are zeros. Any suggestions on how I can push the network to give more weight to the positive classes?
Tensorflow has a loss function weighted_cross_entropy_with_logits, which can be used to give more weight to the 1's. So it should be applicable to a sparse multi-label classification setting like yours.
From the documentation:
This is like sigmoid_cross_entropy_with_logits() except that pos_weight, allows one to trade off recall and precision by up- or down-weighting the cost of a positive error relative to a negative error.
The argument pos_weight is used as a multiplier for the positive targets
If you use the tensorflow backend in Keras, you can use the loss function like this (Keras 2.1.1):
import tensorflow as tf
import keras.backend.tensorflow_backend as tfb
POS_WEIGHT = 10 # multiplier for positive targets, needs to be tuned
def weighted_binary_crossentropy(target, output):
"""
Weighted binary crossentropy between an output tensor
and a target tensor. POS_WEIGHT is used as a multiplier
for the positive targets.
Combination of the following functions:
* keras.losses.binary_crossentropy
* keras.backend.tensorflow_backend.binary_crossentropy
* tf.nn.weighted_cross_entropy_with_logits
"""
# transform back to logits
_epsilon = tfb._to_tensor(tfb.epsilon(), output.dtype.base_dtype)
output = tf.clip_by_value(output, _epsilon, 1 - _epsilon)
output = tf.log(output / (1 - output))
# compute weighted loss
loss = tf.nn.weighted_cross_entropy_with_logits(targets=target,
logits=output,
pos_weight=POS_WEIGHT)
return tf.reduce_mean(loss, axis=-1)
Then in your model:
model.compile(loss=weighted_binary_crossentropy, ...)
I have not found many resources yet which report well working values for the pos_weight in relation to the number of classes, average active classes, etc.
Many thanks to tobigue for the great solution.
The tensorflow and keras apis have changed since that answer. So the updated version of weighted_binary_crossentropy is below for Tensorflow 2.7.0.
import tensorflow as tf
POS_WEIGHT = 10
def weighted_binary_crossentropy(target, output):
"""
Weighted binary crossentropy between an output tensor
and a target tensor. POS_WEIGHT is used as a multiplier
for the positive targets.
Combination of the following functions:
* keras.losses.binary_crossentropy
* keras.backend.tensorflow_backend.binary_crossentropy
* tf.nn.weighted_cross_entropy_with_logits
"""
# transform back to logits
_epsilon = tf.convert_to_tensor(tf.keras.backend.epsilon(), output.dtype.base_dtype)
output = tf.clip_by_value(output, _epsilon, 1 - _epsilon)
output = tf.math.log(output / (1 - output))
loss = tf.nn.weighted_cross_entropy_with_logits(labels=target, logits=output, pos_weight=POS_WEIGHT)
return tf.reduce_mean(loss, axis=-1)