I have a question regarding cross validation in Linear regression model.
From my understanding, in cross validation, we split the data into (say) 10 folds and train the data from 9 folds and the remaining folds we use for testing. We repeat this process until we test all of the folds, so that every folds are tested exactly once.
When we are training the model from 9 folds, should we not get a different model (may be slightly different from the model that we have created when using the whole dataset)? I know that we take an average of all the "n" performances.
But, what about the model? Shouldn't the resulting model also be taken as the average of all the "n" models? I see that the resulting model is same as the model which we created using whole of the dataset before cross-validation. If we are considering the overall model even after cross-validation (and not taking avg of all the models), then what's the point of calculating average performance from n different models (because they are trained from different folds of data and are supposed to be different, right?)
I apologize if my question is not clear or too funny.
Thanks for reading, though!
I think that there is some confusion in some of the answers proposed because of the use of the word "model" in the question asked. If I am guessing correctly, you are referring to the fact that in K-fold cross-validation we learn K-different predictors (or decision functions), which you call "model" (this is a bad idea because in machine learning we also do model selection which is choosing between families of predictors and this is something which can be done using cross-validation). Cross-validation is typically used for hyperparameter selection or to choose between different algorithms or different families of predictors. Once these chosen, the most common approach is to relearn a predictor with the selected hyperparameter and algorithm from all the data.
However, if the loss function which is optimized is convex with respect to the predictor, than it is possible to simply average the different predictors obtained from each fold.
This is because for a convex risk, the risk of the average of the predictor is always smaller than the average of the individual risks.
The PROs and CONs of averaging (vs retraining) are as follows
PROs: (1) In each fold, the evaluation that you made on the held out set gives you an unbiased estimate of the risk for those very predictors that you have obtained, and for these estimates the only source of uncertainty is due to the estimate of the empirical risk (the average of the loss function) on the held out data.
This should be contrasted with the logic which is used when you are retraining and which is that the cross-validation risk is an estimate of the "expected value of the risk of a given learning algorithm" (and not of a given predictor) so that if you relearn from data from the same distribution, you should have in average the same level of performance. But note that this is in average and when retraining from the whole data this could go up or down. In other words, there is an additional source of uncertainty due to the fact that you will retrain.
(2) The hyperparameters have been selected exactly for the number of datapoints that you used in each fold to learn. If you relearn from the whole dataset, the optimal value of the hyperparameter is in theory and in practice not the same anymore, and so in the idea of retraining, you really cross your fingers and hope that the hyperparameters that you have chosen are still fine for your larger dataset.
If you used leave-one-out, there is obviously no concern there, and if the number of data point is large with 10 fold-CV you should be fine. But if you are learning from 25 data points with 5 fold CV, the hyperparameters for 20 points are not really the same as for 25 points...
CONs: Well, intuitively you don't benefit from training with all the data at once
There are unfortunately very little thorough theory on this but the following two papers especially the second paper consider precisely the averaging or aggregation of the predictors from K-fold CV.
Jung, Y. (2016). Efficient Tuning Parameter Selection by Cross-Validated Score in High Dimensional Models. International Journal of Mathematical and Computational Sciences, 10(1), 19-25.
Maillard, G., Arlot, S., & Lerasle, M. (2019). Aggregated Hold-Out. arXiv preprint arXiv:1909.04890.
The answer is simple: you use the process of (repeated) cross validation (CV) to obtain a relatively stable performance estimate for a model instead of improving it.
Think of trying out different model types and parametrizations which are differently well suited for your problem. Using CV you obtain many different estimates on how each model type and parametrization would perform on unseen data. From those results you usually choose one well suited model type + parametrization which you will use, then train it again on all (training) data. The reason for doing this many times (different partitions with repeats, each using different partition splits) is to get a stable estimation of the performance - which will enable you to e.g. look at the mean/median performance and its spread (would give you information about how well the model usually performs and how likely it is to be lucky/unlucky and get better/worse results instead).
Two more things:
Usually, using CV will improve your results in the end - simply because you take a model that is better suited for the job.
You mentioned taking the "average" model. This actually exists as "model averaging", where you average the results of multiple, possibly differently trained models to obtain a single result. Its one way to use an ensemble of models instead of a single one. But also for those you want to use CV in the end for choosing reasonable model.
I like your thinking. I think you have just accidentally discovered Random Forest:
https://en.wikipedia.org/wiki/Random_forest
Without repeated cv your seemingly best model is likely to be only a mediocre model when you score it on new data...
Related
I have an imbalanced data set. My goal is to balance sensitivity and specificity via the confusion matrix. I used glmnet in r with class weights. The model does well at balancing the sensitivity/specificity, but I looked at the calibration plot, and the probabilities are not well calibrated. I have read about calibrating probabilities, but I am wondering if it matters if my goal is to produce class predictions. If it does matter, I have not found a way to calibrate the probabilities when using caret::train().
This topic has been widely discussed, especially in some answers by Stephan Kolassa. I will try to summarize the main take-home messages for your specific question.
From a pure statistical point of view your interest should be on producing as output a probability for each class of any new data instance. As you deal with unbalanced data such probabilities can be small which however - as long as they are correct - is not an issue. Of course, some models can give you poor estimates of the class probabilities. In such cases, the calibration allows you to better calibrate the probabilities obtained from a given model. This means that whenever you estimate for a new observation a probability p of belonging to the target class, then p is indeed its true probability to be of that class.
If you are able to obtain a good probability estimator, then balancing sensitivity or specificity is not part of the statistical part of your problem, but rather of the decision component. Such the final decision will likely need to use some kind of threshold. Depending on the costs of type I and II errors, the cost-optimal threshold might change; however, an optimal decision might also include more than one threshold.
Ultimately, you really have to be careful about which is the specific need of the end-user of your model, because this is what is going to determine the best way of taking decisions using it.
I have calculated the following parameters after applying the following algorithms on a dataset from kaggle
enter image description here
In the above case,linear model is giving the best results.
Are the above results correct and can linear model actually give better results than other 3 in any case?
Or am I missing something?
According to AUC criterion this classification is perfect (1 is theoretical maximum). This means a clear difference in the data. In this case, it makes no sense to talk about differences in the results of methods. Another point is that you can play with methods parameters (you likely will get slightly different results) and other methods can become better. But real result will be indistinguishable. Sophisticated methods are invented for sophisticated data. This is not the case.
All models are wrong, some are useful. - George Box
In terms of classification, a model would be effective as long as it could nicely fit the classification boundaries.
For binary classification case, supposing your data is perfectly linearly separable, then linear model will do the job - actually the "best" job since any more complicated models won't perform better.
If your +'s and -'s are somehow a bit scattered when they cannot be separated by a line (actually hyperplane), then linear model could be beaten by decision tree simply because decision trees can provide classification boundary of more complex shape (cubes).
Then random forest may beat decision tree as classification boundary of random forest is more flexible.
However, as we mentioned early, linear model still has its time.
I am using knn to do classification for a telecom problem. I splitted my data into 70% training and 30% validation. While the knn classifier is able to catch over 80% in 2 deciles in training, its performance in validation sample is as good as random 45 degree line. I am surprised how does KNN work that the model performance in training and validation are so different.
Any pointers ?
Reasonable pointers are hardly possible without more details. The behavior of your KNN depends on several aspects:
The parameter K defining the neighbors. If it is set to K=1, for example, you will get no training error at all, this showing that the consideration of training-to-validation-error may not be justified.
The parameter K is often found using cross validation. I would suggest you to do this as well.
The distance metric. Which function are you using, are there different units, length scales, etc.?
The noise of your data, the size of your data ... -- there simply exist data sets which are hard to describe.
By the way: can you tell what kind of data you want to describe, and, if possible, also provide some examples or show some scatter plot (data and your result)?
I am new to image classification, currently working on SVM(support Vector Machine) method for classifying four groups of images by multisvm function, my algorithm every time the training and testing data are randomly selected and the performance is varies at every time. Some one suggested to do cross validation i did not understand why we need cross validation and what is the main purpose of this? . My actual data set consist training matrix size 28×40000 and testing matrix size 17×40000. how to do cross validation by this data set help me. thanks in advance .
Cross validation is used to select your model. The out-of-sample error can be estimated from your validation error. As a result, you would like to select the model with the least validation error. Here the model refers to the features you want to use, and of more importance, the gamma and C in your SVM. After cross validation, you will use the selected gamma and C with the least average validation error to train the whole training data.
You may also need to estimate the performance of your features and parameters to avoid both high-bias and high-variance. Whether your model suffers underfitting or overfitting can be observed from both in-sample-error and validation error.
Ideally 10-fold is often used for cross validation.
I'm not familiar with multiSVM but you may want to check out libSVM, it is a popular, free SVM library with support for a number of different programming languages.
Here they describe cross validation briefly. It is a way to avoid over-fitting the model by breaking up the training data into sub groups. In this way you can find a model (defined by a set of parameters) which fits both sub groups optimally.
For example, in the following picture they plot the validation accuracy contours for parameterized gamma and C values which are used to define the model. From this contour plot you can tell that the heuristically optimal values (from those tested) are those that give an accuracy closer to 84 instead of 81.
Refer to this link for more detailed information on cross-validation.
You always need to cross-validate your experiments in order to guarantee a correct scientific approach. For instance, if you don't cross-validate, the results you read (such as accuracy) might be highly biased by your test set. In an extreme case, your training step might have been very weak (in terms of fitting data) and your test step might have been very good. This applies to ALL machine learning and optimization experiments, not only SVMs.
To avoid such problems just divide your initial dataset in two (for instance), then train in the first set and test in the second, and repeat the process invesely, training in the second and testing in the first. This will guarantee that any biases to the data are visible to you. As someone suggested, you can perform this with even further division: 10-fold cross-validation, means dividing your data set in 10 parts, then training in 9 and testing in 1, then repeating the process until you have tested in all parts.
I am trying to solve classification problem using Matlab GPTIPS framework.
I managed to build reasonable data representation and fitness function so far and got an average accuracy per class near 65%.
What I need now is some help with two difficulties:
My data is biased. Basically I am solving binary classification problem and only 20% of data belongs to class 1, while other 80% belong to class 0. I used accuracy of prediction as my fitness function at first, but it was really bad. The best I have now is
Fitness = 0.5*(PositivePredictiveValue + NegativePredictiveValue) - const*ComplexityOfSolution
Please, advize, how can I improve my function to make correction for data bias.
Second problem is overfitting. I divided my data into three parts: training (70%), testing (20%), validation (10%). I train each chromosome on training set, then evaluate it's fitness function on testing set. This routine allows me to reach fitness of 0.82 on my test data for the best individual in population. But same individual's result on validation data is only 60%.
I added validation check for best individual each time before new population is generated. Then I compare fitness on validation set with fitness on test set. If difference is more then 5%, then I increase penalty for solution complexity in my fitness function. But it didn't help.
I could also try to evaluate all individuals with validation set during each generation, and simply remove overfitted ones. But then I don't see any difference between my test and validation data. What else can be done here?
UPDATE:
For my second question I've found great article "Experiments on Controlling Overtting
in Genetic Programming" Along with some article authors' ideas on dealing with overfitting in GP it has impressive review with a lot of references to many different approaches to the issue. Now I have a lot of new ideas I can try for my problem.
Unfortunately, still cant' find anything on selecting a proper fitness function which will take into account unbalanced class proportions in my data.
65% accuracy is very bad when the baseline (classify everything as the class with most samples) would be 80%. You need to achieve at least baseline classification in order to have a better model than the naive one.
I would not penalize complexity. Rather limit the tree size (if possible). You could identify simpler models during the run, like storing a pareto front of models with quality and complexity as its two fitness values.
In HeuristicLab we have integrated GP based classification that can do these things. There are several options: You can choose to use MSE for classification or R2. In the latest trunk build there is also an evaluator to optimize accuracy directly (exactly speaking it optimizes the classification penalties). Optimizing MSE means it assigns each class a value (1, 2, 3,...) and tries to minimize mean squared error from that value. This may not seem optimal at first, but works. Optimizing accuracy directly may lead to faster overfitting. There is also a formula simplifier which allows you to prune and shrink your formula (and view the effects of that).
Also, does it need to be GP? Have you tried Random Forest Classification or Support Vector Machines as well? RF are pretty fast and work pretty well usually.