I was using Keras' CNN to classify MNIST dataset. I found that using different batch-sizes gave different accuracies. Why is it so?
Using Batch-size 1000 (Acc = 0.97600)
Using Batch-size 10 (Acc = 0.97599)
Although, the difference is very small, why is there even a difference?
EDIT - I have found that the difference is only because of precision issues and they are in fact equal.
That is because of the Mini-batch gradient descent effect during training process. You can find good explanation Here that I mention some notes from that link here:
Batch size is a slider on the learning process.
Small values give a learning process that converges quickly at the
cost of noise in the training process.
Large values give a learning
process that converges slowly with accurate estimates of the error
gradient.
and also one important note from that link is :
The presented results confirm that using small batch sizes achieves the best training stability and generalization performance, for a
given computational cost, across a wide range of experiments. In all
cases the best results have been obtained with batch sizes m = 32 or
smaller
Which is the result of this paper.
EDIT
I should mention two more points Here:
because of the inherent randomness in machine learning algorithms concept, generally you should not expect machine learning algorithms (like Deep learning algorithms) to have same results on different runs. You can find more details Here.
On the other hand both of your results are too close and somehow they are equal. So in your case we can say that the batch size has no effect on your network results based on the reported results.
This is not connected to Keras. The batch size, together with the learning rate, are critical hyper-parameters for training neural networks with mini-batch stochastic gradient descent (SGD), which entirely affect the learning dynamics and thus the accuracy, the learning speed, etc.
In a nutshell, SGD optimizes the weights of a neural network by iteratively updating them towards the (negative) direction of the gradient of the loss. In mini-batch SGD, the gradient is estimated at each iteration on a subset of the training data. It is a noisy estimation, which helps regularize the model and therefore the size of the batch matters a lot. Besides, the learning rate determines how much the weights are updated at each iteration. Finally, although this may not be obvious, the learning rate and the batch size are related to each other. [paper]
I want to add two points:
1) When use special treatments, it is possible to achieve similar performance for a very large batch size while speeding-up the training process tremendously. For example,
Accurate, Large Minibatch SGD:Training ImageNet in 1 Hour
2) Regarding your MNIST example, I really don't suggest you to over-read these numbers. Because the difference is so subtle that it could be caused by noise. I bet if you try models saved on a different epoch, you will see a different result.
Related
I understand the three types of gradient descent, but my problem is I can not know which type I must use on my model. I have read a lot, but I did not get it.
No code, it is just question.
Types of Gradient Descent:
Batch Gradient Descent: It processes all the training examples for each iteration of gradient descent. But, this method is computationally expensive when the number of training examples is large and usually not preferred.
Stochastic Gradient Descent: It processes one training example in each iteration. Here, the parameters are being updated after each iteration. This method is faster than batch gradient descent method. But, it increases system overhead when number of training examples is large by increasing the number of iterations.
Mini Batch gradient descent: Mini batch algorithm is the most favorable and widely used algorithm that makes precise and faster results using a batch of m training examples. In mini batch algorithm rather than using the complete data set, in every iteration we use a set of m training examples called batch to compute the gradient of the cost function. Common mini-batch sizes range between 50 and 256, but can vary for different applications.
There are various other optimization algorithms apart from gradient descent variants, like adam, rmsprop, etc.
Which optimizer should we use?
The question was to choose the best optimizer for our Neural Network Model in order to converge fast and to learn properly and tune the internal parameters so as to minimize the Loss function.
Adam works well in practice and outperforms other Adaptive techniques.
If your input data is sparse then methods such as SGD, NAG and momentum are inferior and perform poorly. For sparse data sets one should use one of the adaptive learning-rate methods. An additional benefit is that we won't need to adjust the learning rate but likely achieve the best results with the default value.
If one wants fast convergence and train a deep neural network Model or a highly complex Neural Network, then Adam or any other Adaptive learning rate techniques should be used because they outperforms every other optimization algorithms.
I hope this would help you to decide which one to use for your model.
I am working on an article where I focus on a simple problem – linear regression over a large data set in the presence of standard normal or uniform noise. I chose Estimator API from TensorFlow as the modeling framework.
I am finding that, hyperparameter tuning is, in fact, of little importance for such a machine learning problem when the number of training steps can be made sufficiently large. By hyperparameter I mean batch size or number of epochs in the training data stream.
Is there any paper/article with formal proof of this?
I don't think there is a paper specifically focused on this question, because it's a more or less fundamental fact. The introductory chapter of this book discusses the probabilistic interpretation of machine learning in general and loss function optimization in particular.
In short, the idea is this: mini-batch optimization wrt (x1,..., xn) is equivalent to consecutive optimization steps wrt x1, ..., xn inputs, because the gradient is a linear operator. This means that mini-batch update equals to the sum of its individual updates. Important note here: I assume that NN doesn't apply batch-norm or any other layer that adds an explicit variation to the inference model (in this case the math is a bit more hairy).
So the batch size can be seen as a pure computational idea that speeds up the optimization through vectorization and parallel computing. Assuming that one can afford arbitrarily long training and the data are properly shuffled, the batch size can be set to any value. But it isn't automatically true for all hyperparameters, for example very high learning rate can easily force the optimization to diverge, so don't make a mistake thinking hyperparamer tuning isn't important in general.
I implement the ResNet for the cifar 10 in accordance with this document https://arxiv.org/pdf/1512.03385.pdf
But my accuracy is significantly different from the accuracy obtained in the document
My - 86%
Pcs daughter - 94%
What's my mistake?
https://github.com/slavaglaps/ResNet_cifar10
Your question is a little bit too generic, my opinion is that the network is over fitting to the training data set, as you can see the training loss is quite low, but after the epoch 50 the validation loss is not improving anymore.
I didn't read the paper in deep so I don't know how did they solved the problem but increasing regularization might help. The following link will point you in the right direction http://cs231n.github.io/neural-networks-3/
below I copied the summary of the text:
Summary
To train a Neural Network:
Gradient check your implementation with a small batch of data and be aware of the pitfalls.
As a sanity check, make sure your initial loss is reasonable, and that you can achieve 100% training accuracy on a very small portion of
the data
During training, monitor the loss, the training/validation accuracy, and if you’re feeling fancier, the magnitude of updates in relation to
parameter values (it should be ~1e-3), and when dealing with ConvNets,
the first-layer weights.
The two recommended updates to use are either SGD+Nesterov Momentum or Adam.
Decay your learning rate over the period of the training. For example, halve the learning rate after a fixed number of epochs, or
whenever the validation accuracy tops off.
Search for good hyperparameters with random search (not grid search). Stage your search from coarse (wide hyperparameter ranges,
training only for 1-5 epochs), to fine (narrower rangers, training for
many more epochs)
Form model ensembles for extra performance
I would argue that the difference in data pre processing makes the difference in performance. He is using padding and random crops, which in essence increases the amount of training samples and decreases the generalization error. Also as the previous poster said you are missing regularization features, such as the weight decay.
You should take another look at the paper and make sure you implement everything like they did.
The Situation:
I am wondering how to use TensorFlow optimally when my training data is imbalanced in label distribution between 2 labels. For instance, suppose the MNIST tutorial is simplified to only distinguish between 1's and 0's, where all images available to us are either 1's or 0's. This is straightforward to train using the provided TensorFlow tutorials when we have roughly 50% of each type of image to train and test on. But what about the case where 90% of the images available in our data are 0's and only 10% are 1's? I observe that in this case, TensorFlow routinely predicts my entire test set to be 0's, achieving an accuracy of a meaningless 90%.
One strategy I have used to some success is to pick random batches for training that do have an even distribution of 0's and 1's. This approach ensures that I can still use all of my training data and produced decent results, with less than 90% accuracy, but a much more useful classifier. Since accuracy is somewhat useless to me in this case, my metric of choice is typically area under the ROC curve (AUROC), and this produces a result respectably higher than .50.
Questions:
(1) Is the strategy I have described an accepted or optimal way of training on imbalanced data, or is there one that might work better?
(2) Since the accuracy metric is not as useful in the case of imbalanced data, is there another metric that can be maximized by altering the cost function? I can certainly calculate AUROC post-training, but can I train in such a way as to maximize AUROC?
(3) Is there some other alteration I can make to my cost function to improve my results for imbalanced data? Currently, I am using a default suggestion given in TensorFlow tutorials:
cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(pred, y))
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost)
I have heard this may be possible by up-weighting the cost of miscategorizing the smaller label class, but I am unsure of how to do this.
(1)It's ok to use your strategy. I'm working with imbalanced data as well, which I try to use down-sampling and up-sampling methods first to make the training set even distributed. Or using ensemble method to train each classifier with an even distributed subset.
(2)I haven't seen any method to maximise the AUROC. My thought is that AUROC is based on true positive and false positive rate, which doesn't tell how well it works on each instance. Thus, it may not necessarily maximise the capability to separate the classes.
(3)Regarding weighting the cost by the ratio of class instances, it similar to Loss function for class imbalanced binary classifier in Tensor flow
and the answer.
Regarding imbalanced datasets, the first two methods that come to mind are (upweighting positive samples, sampling to achieve balanced batch distributions).
Upweighting positive samples
This refers to increasing the losses of misclassified positive samples when training on datasets that have much fewer positive samples. This incentivizes the ML algorithm to learn parameters that are better for positive samples. For binary classification, there is a simple API in tensorflow that achieves this. See (weighted_cross_entropy) referenced below
https://www.tensorflow.org/api_docs/python/tf/nn/weighted_cross_entropy_with_logits
Batch Sampling
This involves sampling the dataset so that each batch of training data has an even distribution positive samples to negative samples. This can be done using the rejections sampling API provided from tensorflow.
https://www.tensorflow.org/api_docs/python/tf/contrib/training/rejection_sample
I'm one who struggling with imbalanced data. What my strategy to counter imbalanced data are as below.
1) Use cost function calculating 0 and 1 labels at the same time like below.
cost = tf.reduce_mean(-tf.reduce_sum(y*tf.log(_pred) + (1-y)*tf.log(1-_pred), reduction_indices=1))
2) Use SMOTE, oversampling method making number of 0 and 1 labels similar. Refer to here, http://comments.gmane.org/gmane.comp.python.scikit-learn/5278
Both strategy worked when I tried to make credit rating model.
Logistic regression is typical method to handle imbalanced data and binary classification such as predicting default rate. AUROC is one of the best metric to counter imbalanced data.
1) Yes. This is well received strategy to counter imbalanced data. But this strategy is good in Neural Nets only if you using SGD.
Another easy way to balance the training data is using weighted examples. Just amplify the per-instance loss by a larger weight/smaller when seeing imbalanced examples. If you use online gradient descent, it can be as simple as using a larger/smaller learning rate when seeing imbalanced examples.
Not sure about 2.
I'm with a problem when I try to classify my data using libsvm. My training and test data are highly unbalanced. When I do the grid search for the svm parameters and train my data with weights for the classes, the testing gives the accuracy of 96.8113%. But because the testing data is unbalanced, all the correct predicted values are from the negative class, which is larger than the positive class.
I tried a lot of things, from changing the weights until changing the gamma and cost values, but my normalized accuracy (which takes into account the positive classes and negative classes) is lower in each try. Training 50% of positives and 50% of negatives with the default grid.py parameters i have a very low accuracy (18.4234%).
I want to know if the problem is in my description (how to build the feature vectors), in the unbalancing (should i use balanced data in another way?) or should i change my classifier?
Better data always helps.
I think that imbalance is part of the problem. But a more significant part of the problem is how you're evaluating your classifier. Evaluating accuracy given the distribution of positives and negatives in your data is pretty much useless. So is training on 50% and 50% and testing on data that is distributed 99% vs 1%.
There are problems in real life that are like the one your studying (that have a great imbalance in positives to negatives). Let me give you two examples:
Information retrieval: given all documents in a huge collection return the subset that are relevant to search term q.
Face detection: this large image mark all locations where there are human faces.
Many approaches to these type of systems are classifier-based. To evaluate two classifiers two tools are commonly used: ROC curves, Precision Recall curves and the F-score. These tools give a more principled approach to evaluate when one classifier is working better than the another.