I am reading the a deep learning with python book.
After reading chapter 4, Fighting Overfitting, I have two questions.
Why might increasing the number of epochs cause overfitting?
I know increasing increasing the number of epochs will involve more attempts at gradient descent, will this cause overfitting?
During the process of fighting overfitting, will the accuracy be reduced ?
I'm not sure which book you are reading, so some background information may help before I answer the questions specifically.
Firstly, increasing the number of epochs won't necessarily cause overfitting, but it certainly can do. If the learning rate and model parameters are small, it may take many epochs to cause measurable overfitting. That said, it is common for more training to do so.
To keep the question in perspective, it's important to remember that we most commonly use neural networks to build models we can use for prediction (e.g. predicting whether an image contains a particular object or what the value of a variable will be in the next time step).
We build the model by iteratively adjusting weights and biases so that the network can act as a function to translate between input data and predicted outputs. We turn to such models for a number of reasons, often because we just don't know what the function is/should be or the function is too complex to develop analytically. In order for the network to be able to model such complex functions, it must be capable of being highly-complex itself. Whilst this complexity is powerful, it is dangerous! The model can become so complex that it can effectively remember the training data very precisely but then fail to act as an effective, general function that works for data outside of the training set. I.e. it can overfit.
You can think of it as being a bit like someone (the model) who learns to bake by only baking fruit cake (training data) over and over again – soon they'll be able to bake an excellent fruit cake without using a recipe (training), but they probably won't be able to bake a sponge cake (unseen data) very well.
Back to neural networks! Because the risk of overfitting is high with a neural network there are many tools and tricks available to the deep learning engineer to prevent overfitting, such as the use of dropout. These tools and tricks are collectively known as 'regularisation'.
This is why we use development and training strategies involving test datasets – we pretend that the test data is unseen and monitor it during training. You can see an example of this in the plot below (image credit). After about 50 epochs the test error begins to increase as the model has started to 'memorise the training set', despite the training error remaining at its minimum value (often training error will continue to improve).
So, to answer your questions:
Allowing the model to continue training (i.e. more epochs) increases the risk of the weights and biases being tuned to such an extent that the model performs poorly on unseen (or test/validation) data. The model is now just 'memorising the training set'.
Continued epochs may well increase training accuracy, but this doesn't necessarily mean the model's predictions from new data will be accurate – often it actually gets worse. To prevent this, we use a test data set and monitor the test accuracy during training. This allows us to make a more informed decision on whether the model is becoming more accurate for unseen data.
We can use a technique called early stopping, whereby we stop training the model once test accuracy has stopped improving after a small number of epochs. Early stopping can be thought of as another regularisation technique.
More attempts of decent(large number of epochs) can take you very close to the global minima of the loss function ideally, Now since we don't know anything about the test data, fitting the model so precisely to predict the class labels of the train data may cause the model to lose it generalization capabilities(error over unseen data). In a way, no doubt we want to learn the input-output relationship from the train data, but we must not forget that the end goal is for the model to perform well over the unseen data. So, it is a good idea to stay close but not very close to the global minima.
But still, we can ask what if I reach the global minima, what can be the problem with that, why would it cause the model to perform badly on unseen data?
The answer to this can be that in order to reach the global minima we would be trying to fit the maximum amount of train data, this will result in a very complex model(since it is less probable to have a simpler spatial distribution of the selected number of train data that is fortunately available with us). But what we can assume is that a large amount of unseen data(say for facial recognition) will have a simpler spatial distribution and will need a simpler Model for better classification(I mean the entire world of unseen data, will definitely have a pattern that we can't observe just because we have an access small fraction of it in the form of training data)
If you incrementally observe points from a distribution(say 50,100,500, 1000 ...), we will definitely find the structure of the data complex until we have observed a sufficiently large number of points (max: the entire distribution), but once we have observed enough points we can expect to observe the simpler pattern present in the data that can be easily classified.
In short, a small fraction of train data should have a complex structure as compared to the entire dataset. And overfitting to the train data may cause our model to perform worse on the test data.
One analogous example to emphasize the above phenomenon from day to day life is as follows:-
Say we meet N number of people till date in our lifetime, while meeting them we naturally learn from them(we become what we are surrounded with). Now if we are heavily influenced by each individual and try to tune to the behaviour of all the people very closely, we develop a personality that closely resembles the people we have met but on the other hand we start judging every individual who is unlike me -> unlike the people we have already met. Becoming judgemental takes a toll on our capability to tune in with new groups since we trained very hard to minimize the differences with the people we have already met(the training data). This according to me is an excellent example of overfitting and loss in genralazition capabilities.
Related
I'm fairly new to machine learning, and working on optimizing hyperparameters for my model. I'm doing this via a randomized search. My question is: should I be searching over # of epochs and batch size along with my other hyperparameters (e.g. loss function, number of layers, etc.)? If not, should I fix a these values first, find the other parameters, then return to tune these?
My concern is a) that searching over many epochs will be extremely time-consuming, so leaving it at one low value for the initial scan would be useful and b) that these parameters, esp. # of epochs, will disproportionately affect the results when the model is behaving well, and won't really give me much information about the rest of my architecture, as there should be a regime where more epochs, up to a point, are better. I know this isn't totally accurate, i.e. # of epochs is a real hyperparameter and too many can lead to overfitting issues, for example. Currently, my model is not clearly improving with # of epochs, though it was suggested by someone working on a similar problem within my area of research that this may be mitigated by implementing batch normalization, which is another parameter I am testing. Finally, I am worried that batch size will be quite affected by the fact that I am scaling my data down to 60% to allow my code to run reasonably (and I think the final model will be trained on vastly more data than the simulated data currently available to me).
I agree with your intuition on epochs. It is common to keep this value as low as possible in order to complete more training "experiments" in the same number of working hours. I don't have a great reference here, but I would welcome one in the comments.
For almost everything else, there is a paper by Leslie N. Smith that I can't recommend enough, A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decay.
As you can see, batch size is included but epochs are not. You will also notice that the model architecture is not included (number of layers, layer size, etc). Neural Architecture Search is a huge research field in its own right, separate from hyper-parameter tuning.
As for the loss function, I can't think of any reason to "tune" that except in the context of an Auxiliary Loss for training only, which I suspect is not what you are talking about.
The loss function that will be applied to your validation or test set is part of the problem statement. That, along with the data, defines the problem you are solving. You don't changing it by tuning, you change it by convincing a product manager that your alternative is better for the business need.
I have trained a multi-class Random Forest model and So now if the model predicts something wrong we manually correct it, SO the thing is What can we do to with that corrected label and make the predictions better.
Thoughts:
Can't retrain the model again and again.(Trained on 0.7 million rows so it might treat the new data as noise)
Can not train small models of RF as they will also create a mess
Random FOrest works better then NN, So not thinking to go that way.
What do you mean by "manually correct" - i.e. there may be various different points in the decision trees that were executed leading to a wrong prediction, not to mention the numerous decision trees used to get your final prediction.
I think there is some misunderstanding in your first point. Unless the distribution is non-stationary (in which case your trained model is of diminished value to begin with), the new data is treated is treated as "noise" in the sense that including it in the final model is unlikely to change future predictions all that much. As far as I can tell this is how it should be, without specifying other factors like a changing distribution, etc. That is, if future data you want to predict will look a lot more like the data you failed to predict correctly, then you would indeed want to upweight the importance of classifying this sample in your new model.
Anyway, it sounds like you're describing an online learning problem(you want a model that updates itself in response to streaming data). You can find some general ideas just searching for online random forests, for example:
[Online random forests] (http://www.ymer.org/amir/research/online-random-forests/) and [online multiclass lpboost] (https://github.com/amirsaffari/online-multiclass-lpboost) describe a general framework akin to what you may have in mind: the input to the model is a stream of new observations; the forest learns on this new data by dropping those trees which perform poorly and eventually growing new trees that include the new data.
The general idea described here is used in a number of boosting algorithms (for example, AdaBoost aggregates an ensemble of "weak learners", for example individual decision trees grown on different + incomplete subsets of data, into a better whole by training subsequent weak learners specifically on formerly misclassified instances. The idea here is that those instances where your current model is wrong are the most informative for future performance improvements.
I don't know the specific details of how the linked implementations accomplish this, though the idea is inline with what you might expect.
You might try these, or other such algorithms you find from searching around.
That all said, I suspect something like the online random forest algorithm is relatively good when old data becomes obsolete over time. If it doesn't -- i.e. if your future data and early data are pulled from the same distribution -- it's not obvious to me that successively retraining your model (by which I mean the random forest itself and any cross validation / model selection procedures you might have to transform forest predictions into a final assignment) data on the whole batch of examples you have is a bad idea, modulo data in a very high dimensional feature space, or really quickly incoming data.
For a class project, I designed a neural network to approximate sin(x), but ended up with a NN that just memorized my function over the data points I gave it. My NN took in x-values with a batch size of 200. Each x-value was multiplied by 200 different weights, mapping to 200 different neurons in my first layer. My first hidden layer contained 200 neurons, each one a linear combination of the x-values in the batch. My second hidden layer also contained 200 neurons, and my loss function was computed between the 200 neurons in my second layer and the 200 values of sin(x) that the input mapped to.
The problem is, my NN perfectly "approximated" sin(x) with 0 loss, but I know it wouldn't generalize to other data points.
What did I do wrong in designing this neural network, and how can I avoid memorization and instead design my NN's to "learn" about the patterns in my data?
It is same with any machine learning algorithm. You have a dataset based on which you try to learn "the" function f(x), which actually generated the data. In real life datasets, it is impossible to get the original function from the data, and therefore we approximate it using something g(x).
The main goal of any machine learning algorithm is to predict unseen data as best as possible using the function g(x).
Given a dataset D you can always train a model, which will perfectly classify all the datapoints (you can use a hashmap to get 0 error on the train set), but which is overfitting or memorization.
To avoid such things, you yourself have to make sure that the model does not memorise and learns the function. There are a few things which can be done. I am trying to write them down in an informal way (with links).
Train, Validation, Test
If you have large enough dataset, use Train, Validation, Test splits. Split the dataset in three parts. Typically 60%, 20% and 20% for Training, Validation and Test, respectively. (These numbers can vary based on need, also in case of imbalanced data, check how to get stratified partitions which preserve the class ratios in every split). Next, forget about the Test partition, keep it somewhere safe, don't touch it. Your model, will be trained using the Training partition. Once you have trained the model, evaluate the performance of the model using the Validation set. Then select another set of hyper-parameter configuration for your model (eg. number of hidden layer, learaning algorithm, other parameters etc.) and then train the model again, and evaluate based on Validation set. Keep on doing this for several such models. Then select the model, which got you the best validation score.
The role of validation set here is to check what the model has learned. If the model has overfit, then the validation scores will be very bad, and therefore in the above process you will discard those overfit models. But keep in mind, although you did not use the Validation set to train the model, directly, but the Validation set was used indirectly to select the model.
Once you have selected a final model based on Validation set. Now take out your Test set, as if you just got new dataset from real life, which no one has ever seen. The prediction of the model on this Test set will be an indication how well your model has "learned" as it is now trying to predict datapoints which it has never seen (directly or indirectly).
It is key to not go back and tune your model based on the Test score. This is because once you do this, the Test set will start contributing to your mode.
Crossvalidation and bootstrap sampling
On the other hand, if your dataset is small. You can use bootstrap sampling, or k-fold cross-validation. These ideas are similar. For example, for k-fold cross-validation, if k=5, then you split the dataset in 5 parts (also be carefull about stratified sampling). Let's name the parts a,b,c,d,e. Use the partitions [a,b,c,d] to train and get the prediction scores on [e] only. Next, use the partitions [a,b,c,e] and use the prediction scores on [d] only, and continue 5 times, where each time, you keep one partition alone and train the model with the other 4. After this, take an average of these scores. This is indicative of that your model might perform if it sees new data. It is also a good practice to do this multiple times and perform an average. For example, for smaller datasets, perform a 10 time 10-folds cross-validation, which will give a pretty stable score (depending on the dataset) which will be indicative of the prediction performance.
Bootstrap sampling is similar, but you need to sample the same number of datapoints (depends) with replacement from the dataset and use this sample to train. This set will have some datapoints repeated (as it was a sample with replacement). Then use the missing datapoins from the training dataset to evaluate the model. Perform this multiple times and average the performance.
Others
Other ways are to incorporate regularisation techniques in the classifier cost function itself. For example in Support Vector Machines, the cost function enforces conditions such that the decision boundary maintains a "margin" or a gap between two class regions. In neural networks one can also do similar things (although it is not same as in SVM).
In neural network you can use early stopping to stop the training. What this does, is train on the Train dataset, but at each epoch, it evaluates the performance on the Validation dataset. If the model starts to overfit from a specific epoch, then the error for Training dataset will keep on decreasing, but the error of the Validation dataset will start increasing, indicating that your model is overfitting. Based on this one can stop training.
A large dataset from real world tends not to overfit too much (citation needed). Also, if you have too many parameters in your model (to many hidden units and layers), and if the model is unnecessarily complex, it will tend to overfit. A model with lesser pameter will never overfit (though can underfit, if parameters are too low).
In the case of you sin function task, the neural net has to overfit, as it is ... the sin function. These tests can really help debug and experiment with your code.
Another important note, if you try to do a Train, Validation, Test, or k-fold crossvalidation on the data generated by the sin function dataset, then splitting it in the "usual" way will not work as in this case we are dealing with a time-series, and for those cases, one can use techniques mentioned here
First of all, I think it's a great project to approximate sin(x). It would be great if you could share the snippet or some additional details so that we could pin point the exact problem.
However, I think that the problem is that you are overfitting the data hence you are not able to generalize well to other data points.
Few tricks that might work,
Get more training points
Go for regularization
Add a test set so that you know whether you are overfitting or not.
Keep in mind that 0 loss or 100% accuracy is mostly not good on training set.
I'm trying to automatically determine when a Keras autoencoder converges. For example, look at this link under "Let's build the simplest autoencoder possible." The number of epochs is hardcoded at 50 (when the loss value converges). However, how would you code this using Keras if you didn't know the number was 50? Would you just keep calling fit()?
This question is actually ridiculously wide and hard. There are many techniques on how to set the number of epochs:
Early stopping- in this case you set the number of epochs to a really high number and you turn off the training when the improvement over next epochs is not satisfying. In Keras you have a special object called EarlyStopping which does the job for you.
Model Checkpoint - here you once again set up a really high number of epochs and you simply save only the best model w.r.t. to a metric chosen. Once again you have a special callback for this scenario.
Of course, there are other scenarios like e.g. using Reinforcement learning to find the stopping time or more complexed scenarios when you choose this in a Bayesian hyperparameter set up but those are much harder methods which are often not introducing any improvement.
One sure thing is that restarting a fit method might end up in unexpected behaviour as many inner states of a model are reset which could cause instability. For this scenario I strongly advise you to use train_on_batch which is not resetting model states and makes a lot of fancy training scenarios possible.
I know you're supposed to separate your training data from your testing data, but when you make predictions with your model is it OK to use the entire data set?
I assume separating your training and testing data is valuable for assessing the accuracy and prediction strength of different models, but once you've chosen a model I can't think of any downsides to using the full data set for predictions.
You can use full data for prediction but better retain indexes of train and test data. Here are pros and cons of it:
Pro:
If you retain index of rows belonging to train and test data then you just need to predict once (and so time saving) to get all results. You can calculate performance indicators (R2/MAE/AUC/F1/precision/recall etc.) for train and test data separately after subsetting actual and predicted value using train and test set indexes.
Cons:
If you calculate performance indicator for entire data set (not clearly differentiating train and test using indexes) then you will have overly optimistic estimates. This happens because (having trained on train data) model gives good results of train data. Which depending of % split of train and test, will gives illusionary good performance indicator values.
Processing large test data at once may create memory bulge which is can result in crash in all-objects-in-memory languages like R.
In general, you're right - when you've finished selecting your model and tuning the parameters, you should use all of your data to actually build the model (exception below).
The reason for dividing data into train and test is that, without out-of-bag samples, high-variance algorithms will do better than low-variance ones, almost by definition. Consequently, it's necessary to split data into train and test parts for questions such as:
deciding whether kernel-SVR is better or worse than linear regression, for your data
tuning the parameters of kernel-SVR
However, once these questions are determined, then, in general, as long as your data is generated by the same process, the better predictions will be, and you should use all of it.
An exception is the case where the data is, say, non-stationary. Suppose you're training for the stock market, and you have data from 10 years ago. It is unclear that the process hasn't changed in the meantime. You might be harming your prediction, by including more data, in this case.
Yes, there are techniques for doing this, e.g. k-fold cross-validation:
One of the main reasons for using cross-validation instead of using the conventional validation (e.g. partitioning the data set into two sets of 70% for training and 30% for test) is that there is not enough data available to partition it into separate training and test sets without losing significant modelling or testing capability. In these cases, a fair way to properly estimate model prediction performance is to use cross-validation as a powerful general technique.
That said, there may not be a good reason for doing so if you have plenty of data, because it means that the model you're using hasn't actually been tested on real data. You're inferring that it probably will perform well, since models trained using the same methods on less data also performed well. That's not always a safe assumption. Machine learning algorithms can be sensitive in ways you wouldn't expect a priori. Unless you're very starved for data, there's really no reason for it.