I am very new to neural networks. I have a dataset that contains 16M records, in which only 70K are labeled 1 and the rest are 0 (even by setting some special restrictions the total would not be less than 2.5M records in which 58K is labeled 1, and the restriction is not fully logical as well). Is there any special practice to deal with this kind of data?
Now if I just write a function to always return 0, the accuracy would be 99.56% ! Is neural network an appropriate option at all? If no, what is my alternative and if yes, how should deal with it?
tnx
You can try to give a higher weight to samples labeled 1 or sample minibatches from both classes separately, such that the network is shown the same number of examples from both classes.
For the first method, frameworks such as Keras give an option to include a weight factor for every class:
class_weights = {
0: 1.0,
1: 43.0,
}
model.fit(X, y, ..., class_weight=class_weights)
scikit-learn has a method of computing the class weights automatically, as shown in this comment on Kaggle
Accuracy is not a good way to measure the performance of the network in this case. Precision, recall for the class 1 or similar measures might give a better understanding of the performance of the model.
Related
Hello and thanks for helping,
My question is a long time problem that I try to tackle :
How do we train a neural network if the input is a probability rather than a value ?
To make it more intuitive :
Let's say we have 6 features and the value they may take is 1 or -1 for each.
Their value is determined probabilistically, such as the feature 1 can be 1 with 60% probability or -1 with 30% probability.
How do we train the network if in each trial, we may get a INPUT value in accordance with the probability distribution of each feature ?
Actually the answer is more straingthforward than you might expect, as many existing neural networks are actually trained exactly in this manner. You have to do ... nothing. Simply sample your batch in each iteration according to your distribution and that's all. Neural network does not require finite training set, thus you can efficiently train it on "potentialy ifinite" one (generator of samples). This is exactly what is being done in image processing with image augmentation - each batch consists random subsamples of the images (patches), which are sampled from very basic probability distributions.
#Nagabuhushan suggests solving different problem - where you know a priori probability of each sample, which, according to question is not the case:
we may get a INPUT value in accordance with the probability distribution of each feature
Plus, even if it would be the case, NNs are not good with multiplying thus one might need additional tweaking of architecture (log-transforms).
For the values you feed into the net, you should use the probabilities of each feature taking on the value 1. You could use the probabilities of them taking on -1, but be consistent. Also, determine some order of features and consistently order their probabilities, respectively.
Edit: I think I may have misunderstood the question. Do your inputs consist of probabilities, or 1's and -1's? If the latter, then a well-architected network should learn the distributions on its own. Just be sure to train it against the same input space that you'll be evaluating it against.
Most examples of neural networks for classification tasks I've seen use the a softmax layer as output activation function. Normally, the other hidden units use a sigmoid, tanh, or ReLu function as activation function. Using the softmax function here would - as far as I know - work out mathematically too.
What are the theoretical justifications for not using the softmax function as hidden layer activation functions?
Are there any publications about this, something to quote?
I haven't found any publications about why using softmax as an activation in a hidden layer is not the best idea (except Quora question which you probably have already read) but I will try to explain why it is not the best idea to use it in this case :
1. Variables independence : a lot of regularization and effort is put to keep your variables independent, uncorrelated and quite sparse. If you use softmax layer as a hidden layer - then you will keep all your nodes (hidden variables) linearly dependent which may result in many problems and poor generalization.
2. Training issues : try to imagine that to make your network working better you have to make a part of activations from your hidden layer a little bit lower. Then - automaticaly you are making rest of them to have mean activation on a higher level which might in fact increase the error and harm your training phase.
3. Mathematical issues : by creating constrains on activations of your model you decrease the expressive power of your model without any logical explaination. The strive for having all activations the same is not worth it in my opinion.
4. Batch normalization does it better : one may consider the fact that constant mean output from a network may be useful for training. But on the other hand a technique called Batch Normalization has been already proven to work better, whereas it was reported that setting softmax as activation function in hidden layer may decrease the accuracy and the speed of learning.
Actually, Softmax functions are already used deep within neural networks, in certain cases, when dealing with differentiable memory and with attention mechanisms!
Softmax layers can be used within neural networks such as in Neural Turing Machines (NTM) and an improvement of those which are Differentiable Neural Computer (DNC).
To summarize, those architectures are RNNs/LSTMs which have been modified to contain a differentiable (neural) memory matrix which is possible to write and access through time steps.
Quickly explained, the softmax function here enables a normalization of a fetch of the memory and other similar quirks for content-based addressing of the memory. About that, I really liked this article which illustrates the operations in an NTM and other recent RNN architectures with interactive figures.
Moreover, Softmax is used in attention mechanisms for, say, machine translation, such as in this paper. There, the Softmax enables a normalization of the places to where attention is distributed in order to "softly" retain the maximal place to pay attention to: that is, to also pay a little bit of attention to elsewhere in a soft manner. However, this could be considered like to be a mini-neural network that deals with attention, within the big one, as explained in the paper. Therefore, it could be debated whether or not Softmax is used only at the end of neural networks.
Hope it helps!
Edit - More recently, it's even possible to see Neural Machine Translation (NMT) models where only attention (with softmax) is used, without any RNN nor CNN: http://nlp.seas.harvard.edu/2018/04/03/attention.html
Use a softmax activation wherever you want to model a multinomial distribution. This may be (usually) an output layer y, but can also be an intermediate layer, say a multinomial latent variable z. As mentioned in this thread for outputs {o_i}, sum({o_i}) = 1 is a linear dependency, which is intentional at this layer. Additional layers may provide desired sparsity and/or feature independence downstream.
Page 198 of Deep Learning (Goodfellow, Bengio, Courville)
Any time we wish to represent a probability distribution over a discrete variable with n possible values, we may use the softmax function. This can be seen as a generalization of the sigmoid function which was used to represent a probability
distribution over a binary variable.
Softmax functions are most often used as the output of a classifier, to represent the probability distribution over n different classes. More rarely, softmax functions can be used inside the model itself, if we wish the model to choose between one of n different options for some internal variable.
Softmax function is used for the output layer only (at least in most cases) to ensure that the sum of the components of output vector is equal to 1 (for clarity see the formula of softmax cost function). This also implies what is the probability of occurrence of each component (class) of the output and hence sum of the probabilities(or output components) is equal to 1.
Softmax function is one of the most important output function used in deep learning within the neural networks (see Understanding Softmax in minute by Uniqtech). The Softmax function is apply where there are three or more classes of outcomes. The softmax formula takes the e raised to the exponent score of each value score and devide it by the sum of e raised the exponent scores values. For example, if I know the Logit scores of these four classes to be: [3.00, 2.0, 1.00, 0.10], in order to obtain the probabilities outputs, the softmax function can be apply as follows:
import numpy as np
def softmax(x):
z = np.exp(x - np.max(x))
return z / z.sum()
scores = [3.00, 2.0, 1.00, 0.10]
print(softmax(scores))
Output: probabilities (p) = 0.642 0.236 0.087 0.035
The sum of all probabilities (p) = 0.642 + 0.236 + 0.087 + 0.035 = 1.00. You can try to substitute any value you know in the above scores, and you will get a different values. The sum of all the values or probabilities will be equal to one. That’s makes sense, because the sum of all probability is equal to one, thereby turning Logit scores to probability scores, so that we can predict better. Finally, the softmax output, can help us to understand and interpret Multinomial Logit Model. If you like the thoughts, please leave your comments below.
I have data set for classification problem. I have in total 50 classes.
Class1: 10,000 examples
Class2: 10 examples
Class3: 5 examples
Class4: 35 examples
.
.
.
and so on.
I tried to train my classifier using SVM ( both linear and Gaussian kernel). My accurate is very bad on test data 65 and 72% respectively. Now I am thinking to go for a neural network. Do you have any suggestion for any machine learning model and algorithm for large imbalanced data? It would be extremely helpful to me
You should provide more information about the data set features and the class distribution, this would help others to advice you.
In any case, I don't think a neural network fits here as this data set is too small for it.
Assuming 50% or more of the samples are of class 1 then I would first start by looking for a classifier that differentiates between class 1 and non-class 1 samples (binary classification). This classifier should outperform a naive classifier (benchmark) which randomly chooses a classification with a prior corresponding to the training set class distribution.
For example, assuming there are 1,000 samples, out of which 700 are of class 1, then the benchmark classifier would classify a new sample as class 1 in a probability of 700/1,000=0.7 (like an unfair coin toss).
Once you found a classifier with good accuracy, the next phase can be classifying the non-class 1 classified samples as one of the other 49 classes, assuming these classes are more balanced then I would start with RF, NB and KNN.
There are multiple ways to handle with imbalanced datasets, you can try
Up sampling
Down Sampling
Class Weights
I would suggest either Up sampling or providing class weights to balance it
https://towardsdatascience.com/5-techniques-to-work-with-imbalanced-data-in-machine-learning-80836d45d30c
You should think about your performance metric, don't use Accuracy score as your performance metric , You can use Log loss or any other suitable metric
https://machinelearningmastery.com/failure-of-accuracy-for-imbalanced-class-distributions/
From my experience the most successful ways to deal with unbalanced classes are :
Changing distribiution of inputs: 20000 samples (the approximate number of examples which you have) is not a big number so you could change your dataset distribiution simply by using every sample from less frequent classes multiple times. Depending on a number of classes you could set the number of examples from them to e.g. 6000 or 8000 each in your training set. In this case remember to not change distribiution on test and validation set.
Increase the time of training: in case of neural networks, when changing distribiution of your input is impossible I strongly advise you trying to learn network for quite a long time (e.g. 1000 epochs). In this case you have to remember about regularisation. I usually use dropout and l2 weight regulariser with their parameters learnt by random search algorithm.
Reduce the batch size: In neural networks case reducing a batch size might lead to improving performance on less frequent classes.
Change your loss function: using MAPE insted of Crossentropy may also improve accuracy on less frequent classes.
Feel invited to test different combinations of approaches shown by e.g. random search algorithm.
Data-level methods:
Undersampling runs the risk of losing important data from removing data. Oversampling runs the risk of overfitting on training data, especially if the added copies of the minority class are replicas of existing data. Many sophisticated sampling techniques have been developed to mitigate these risks.
One such technique is two-phase learning. You first train your model on the resampled data. This resampled data can be achieved by randomly undersampling large classes until each class has only N instances. You then fine-tune your model on the original data.
Another technique is dynamic sampling: oversample the low-performing classes and undersample the high-performing classes during the training process. Introduced by Pouyanfar et al., the method aims to show the model less of what it has already learned and more of what it has not.
Algorithm-level methods
Cost-sensitive learning
Class-balanced loss
Focal loss
References:
esigning Machine Learning Systems
Survey on deep learning with class imbalance
I have a minimal example of a neural network with a back-propagation trainer, testing it on the IRIS data set. I started of with 7 hidden nodes and it worked well.
I lowered the number of nodes in the hidden layer to 1 (expecting it to fail), but was surprised to see that the accuracy went up.
I set up the experiment in azure ml, just to validate that it wasn't my code. Same thing there, 98.3333% accuracy with a single hidden node.
Can anyone explain to me what is happening here?
First, it has been well established that a variety of classification models yield incredibly good results on Iris (Iris is very predictable); see here, for example.
Secondly, we can observe that there are relatively few features in the Iris dataset. Moreover, if you look at the dataset description you can see that two of the features are very highly correlated with the class outcomes.
These correlation values are linear, single-feature correlations, which indicates that one can most likely apply a linear model and observe good results. Neural nets are highly nonlinear; they become more and more complex and capture greater and greater nonlinear feature combinations as the number of hidden nodes and hidden layers is increased.
Taking these facts into account, that (a) there are few features to begin with and (b) that there are high linear correlations with class, would all point to a less complex, linear function as being the appropriate predictive model-- by using a single hidden node, you are very nearly using a linear model.
It can also be noted that, in the absence of any hidden layer (i.e., just input and output nodes), and when the logistic transfer function is used, this is equivalent to logistic regression.
Just adding to DMlash's very good answer: The Iris data set can even be predicted with a very high accuracy (96%) by using just three simple rules on only one attribute:
If Petal.Width = (0.0976,0.791] then Species = setosa
If Petal.Width = (0.791,1.63] then Species = versicolor
If Petal.Width = (1.63,2.5] then Species = virginica
In general neural networks are black boxes where you never really know what they are learning but in this case back-engineering should be easy. It is conceivable that it learnt something like the above.
The above rules were found by using the OneR package.
I have a binary class dataset (0 / 1) with a large skew towards the "0" class (about 30000 vs 1500). There are 7 features for each instance, no missing values.
When I use the J48 or any other tree classifier, I get almost all of the "1" instances misclassified as "0".
Setting the classifier to "unpruned", setting minimum number of instances per leaf to 1, setting confidence factor to 1, adding a dummy attribute with instance ID number - all of this didn't help.
I just can't create a model that overfits my data!
I've also tried almost all of the other classifiers Weka provides, but got similar results.
Using IB1 gets 100% accuracy (trainset on trainset) so it's not a problem of multiple instances with the same feature values and different classes.
How can I create a completely unpruned tree?
Or otherwise force Weka to overfit my data?
Thanks.
Update: Okay, this is absurd. I've used only about 3100 negative and 1200 positive examples, and this is the tree I got (unpruned!):
J48 unpruned tree
------------------
F <= 0.90747: 1 (201.0/54.0)
F > 0.90747: 0 (4153.0/1062.0)
Needless to say, IB1 still gives 100% precision.
Update 2: Don't know how I missed it - unpruned SimpleCart works and gives 100% accuracy train on train; pruned SimpleCart is not as biased as J48 and has a decent false positive and negative ratio.
Weka contains two meta-classifiers of interest:
weka.classifiers.meta.CostSensitiveClassifier
weka.classifiers.meta.MetaCost
They allows you to make any algorithm cost-sensitive (not restricted to SVM) and to specify a cost matrix (penalty of the various errors); you would give a higher penalty for misclassifying 1 instances as 0 than you would give for erroneously classifying 0 as 1.
The result is that the algorithm would then try to:
minimize expected misclassification cost (rather than the most likely class)
The quick and dirty solution is to resample. Throw away all but 1500 of your positive examples and train on a balanced data set. I am pretty sure there is a resample component in Weka to do this.
The other solution is to use a classifier with a variable cost for each class. I'm pretty sure libSVM allows you to do this and I know Weka can wrap libSVM. However I haven't used Weka in a while so I can't be of much practical help here.