I was reading about cross validation and about how it it is used to select the best model and estimate parameters , I did not really understand the meaning of it.
Suppose I build a Linear regression model and go for a 10 fold cross validation, I think each of the 10 will have different coefficiant values , now from 10 different which should I pick as my final model or estimate parameters.
Or do we use Cross Validation only for the purpose of finding an average error(average of 10 models in our case) and comparing against another model ?
If your build a Linear regression model and go for a 10 fold cross validation, indeed each of the 10 will have different coefficient values. The reason why you use cross validation is that you get a robust idea of the error of your linear model - rather than just evaluating it on one train/test split only, which could be unfortunate or too lucky. CV is more robust as no ten splits can be all ten lucky or all ten unfortunate.
Your final model is then trained on the whole training set - this is where your final coefficients come from.
Cross-validation is used to see how good your models prediction is. It's pretty smart making multiple tests on the same data by splitting it as you probably know (i.e. if you don't have enough training data this is good to use).
As an example it might be used to make sure you aren't overfitting the function. So basically you try your function when you've finished it with Cross-validation and if you see that the error grows a lot somewhere you go back to tweaking the parameters.
Edit:
Read the wikipedia for deeper understanding of how it works: https://en.wikipedia.org/wiki/Cross-validation_%28statistics%29
You are basically confusing Grid-search with cross-validation. The idea behind cross-validation is basically to check how well a model will perform in say a real world application. So we basically try randomly splitting the data in different proportions and validate it's performance. It should be noted that the parameters of the model remain the same throughout the cross-validation process.
In Grid-search we try to find the best possible parameters that would give the best results over a specific split of data (say 70% train and 30% test). So in this case, for different combinations of the same model, the dataset remains constant.
Read more about cross-validation here.
Cross Validation is mainly used for the comparison of different models.
For each model, you may get the average generalization error on the k validation sets. Then you will be able to choose the model with the lowest average generation error as your optimal model.
Cross-Validation or CV allows us to compare different machine learning methods and get a sense of how well they will work in practice.
Scenario-1 (Directly related to the question)
Yes, CV can be used to know which method (SVM, Random Forest, etc) will perform best and we can pick that method to work further.
(From these methods different models will be generated and evaluated for each method and an average metric is calculated for each method and the best average metric will help in selecting the method)
After getting the information about the best method/ or best parameters we can train/retrain our model on the training dataset.
For parameters or coefficients, these can be determined by grid search techniques. See grid search
Scenario-2:
Suppose you have a small amount of data and you want to perform training, validation and testing on data. Then dividing such a small amount of data into three sets reduce the training samples drastically and the result will depend on the choice of pairs of training and validation sets.
CV will come to the rescue here. In this case, we don't need the validation set but we still need to hold the test data.
A model will be trained on k-1 folds of training data and the remaining 1 fold will be used for validating the data. A mean and standard deviation metric will be generated to see how well the model will perform in practice.
Related
I'm doing hyperparameter tuning across multiple models and comparing the results. The hyperparameters of each model are chosen by 5-fold cross-validation. I'm using the sklearn.model_selection.KFold(n_splits=5, shuffle=True) function to get a fold generator.
After checking the documentation on KFold and the source code of some models, I suspect a new set of folds is created for each model. I want to make things more fair and use the same (initially random) folds for all the models I'm tuning. Is there a way to do this in scikit-learn?
As a related question, does it make sense to use the same folds to obtain this fair comparison I'm trying to do?
You have two options:
Shuffle your data at the begining, then use Kfold with shuffle=False.
Set the parameter random_state equal to the same integer each time you perform KFold.
Either option should result in using the same folds when you repeat KFold. See the documentation here: https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html
This approach makes logical sense to me, but I wouldn't expect it to make a significant difference. Perhaps someone else can give a more detailed explanation of the advantages / disadvantages.
The goal of cross-validation is to obtain a representative measure of the accuracy in the test set. The more fold you have the more accurate your metric will be.
If you are using 5 or 10 fold cross-validation to compare different sets of hyperparameters, you don't have to use the exact same splits to compare your models. The average accuracy of all folds will give you a good idea how the model is performing and will allow you to compare them.
I have a model tuning object that fits multiple models and tunes each one of them to find the best hyperparameter combination for each of the models. I want to perform cross-validation on the model tuning part and this is where I am facing a dilemma.
Let's assume that I am fitting just the one model- a random forest classifier and performing a 5 fold cross-validation. Currently, for the first fold that I leave out, I fit the random forest model and perform the model tuning. I am performing model tuning using the dlib package. I calculate the evaluation metric(accuracy, precision, etc) and select the best hyper-parameter combination.
Now when I am leaving out the second fold, should I be tuning the model again? Because if I do, I will get a different combination of hyperparameters than I did in the first case. If I do this across the five folds, what combination do I select?
The cross validators present in spark and sklearn use grid search so for each fold they have the same hyper-parameter combination and don't have to bother about hyper-parameter combinations changing across folds
Choosing the best hyper-parameter combination that I get when I leave out the first fold and using it for the subsequent folds doesn't sound right because then my entire model tuning is dependent on which fold got left out first. However, if I am getting different hyperparameters each time, which one do I settle on?
TLDR:
If you are performing let's say a derivative based model tuning along with cross-validation, your hyper-parameter combination changes as you iterate over folds. How do you select the best combination then? Generally speaking, how do you use cross-validation with derivative-based model tuning methods.
PS: Please let me know if you need more details
This is more of a comment, but it is too long for this, so I post it as an answer instead.
Cross-validation and hyperparameter tuning are two separate things. Cross Validation is done to get a sense of the out-of-sample prediction error of the model. You can do this by having a dedicated validation set, but this raises the question if you are overfitting to this particular validation data. As a consequence, we often use cross-validation where the data are split in to k folds and each fold is used once for validation while the others are used for fitting. After you have done this for each fold, you combine the prediction errors into a single metric (e.g. by averaging the error from each fold). This then tells you something about the expected performance on unseen data, for a given set of hyperparameters.
Once you have this single metric, you can change your hyperparameter, repeat, and see if you get a lower error with the new hyperparameter. This is the hpyerparameter tuning part. The CV part is just about getting a good estimate of the model performance for the given set of hyperparameters, i.e. you do not change hyperparameters 'between' folds.
I think one source of confusion might be the distinction between hyperparameters and parameters (sometimes also referred to as 'weights', 'feature importances', 'coefficients', etc). If you use a gradient-based optimization approach, these change between iterations until convergence or a stopping rule is reached. This is however different from hyperparameter search (e.g. how many trees to plant in the random forest?).
By the way, I think questions like these should better be posted to the Cross-Validated or Data Science section here on StackOverflow.
When evaluating a recommender system, one could split his data into three pieces: training, validation and testing sets. In such case, the training set would be used to learn the recommendation model from data and the validation set would be used to choose the best model or parameters to use. Then, using the chosen model, the user could evaluate the performance of his algorithm using the testing set.
I have found a documentation page for the scikit-learn cross validation (http://scikit-learn.org/stable/modules/cross_validation.html) where it says that is not necessary to split the data into three pieces when using k-fold-cross validation, but only into two: training and testing.
A solution to this problem is a procedure called cross-validation (CV for short). A test set should still be held out for final evaluation, but the validation set is no longer needed when doing CV. In the basic approach, called k-fold CV, the training set is split into k smaller sets (other approaches are described below, but generally follow the same principles).
I am wondering if this would be a good approach. And if so, someone could show me a reference to an article/book backing this theory up?
Cross validation does not avoid validation set, it simply uses many. In other words instead of one split into three parts, you have one split into two, and what you now call "training" is actually what previously has been training and validation, CV is simply about repeated splits (in slightly more smart manner than just randomly) into train and test, and then averaging the results. Theory backing it up is widely available in pretty much any good ML book; the crucial bit is "should I use it" and the answer is suprisingly simple - only if you do not have enough data to do one split. CV is used when you do not have enough data for each of the splits to be representative for the distribution you are interested in, then doing repeated splits simply reduce the variance. Furthermore, for really small datasets one does nested CV - one for [train+val][test] split and internal for [train][val], so the variance of both - model selection and its final evaluation - are reduced.
I built a hurdle model, and then used that model to predict from known to unknown data points using the predict command. Is there a way to validate the model and these predictions? Do I have to do this in two parts, for example using sensitivity and specificity for the binomial part of the model?
Any other ideas for how to assess the validity of this model?
For validating predictive models, I usually trust Cross-Validation.
In short: With cross-validation you can measure the predictive performance of your model using only the training data (data with known results). Thus you can get a general opinion on how your model works. Cross-validation works quite well for wide variety of different models. The downside is that it can get quite computation heavy.
With large data sets, 10-fold cross-validation is enough. The smaller your dataset is, the more "folds" you have to do (i.e. with very small datasets, you have to do leave-one-out cross-validation)
With cross-validation, you get predictions for the whole data set. You can then compare these predictions to the actual outputs and measure how well your model performed.
Cross-validated results can take a bit to understand in more complicated comparisons, but for your general purpose question "how to assess the validity of the model", the results should be quite easy to use.
So I trying to perform a 4-fold cross validation on my training set. I have divided my training data into four quarters. I use three quarters for training and one quarter for validation. I repeat this three more times till all the quarters are given a chance to be the validation set, atleast once.
Now after training I have four caffemodels. I test the models on my validation sets. I am getting different accuracy in each case. How should I proceed from here? Should I just choose the model with the highest accuracy?
Maybe it is a late reply, but in any case...
The short answer is that, if the performances of the four models are similar and good enough, then you re-train the model on all the data available, because you don't want to waste any of them.
The n-fold cross validation is a practical technique to get some insights on the learning and generalization properties of the model you are trying to train, when you don't have a lot of data to start with. You can find details everywhere on the web, but I suggest the open-source book Introduction to Statistical Learning, Chapter 5.
The general rule says that after you trained your n models, you average the prediction error (MSE, accuracy, or whatever) to get a general idea of the performance of that particular model (in your case maybe the network architecture and learning strategy) on that dataset.
The main idea is to assess the models learned on the training splits checking if they have an acceptable performance on the validation set. If they do not, then your models probably overfitted tha training data. If both the errors on training and validation splits are high, then the models should be reconsidered, since they don't have predictive capacity.
In any case, I would also consider the advice of Yoshua Bengio who says that for the kind of problem deep learning is meant for, you usually have enough data to simply go with a training/test split. In this case this answer on Stackoverflow could be useful to you.