I have never seen such learning curves. Am I right, that huge overfitting occurs? The model is fitting better and better to the training data, while it generalizes worse for the test data.
Usually when there is high variance, like here, more examples should help. In this case, they won't, I suspect. Why is that? Why such example of learning curves can't be found easily in literature/tutorials?
Learning curves. SVM, param1 is C, param2 is gamma
You have to remember that SVM is non parametric model, thus more samples does not have to reduce variance. Reduction in variance can be more or less guaranteed for parametric model (like neural net), but SVM is not one of them - more samples mean not only better training data but also more complex model. Your learning curves are typical example of SVM overfitting, which happens a lot with RBF kernel.
Related
I am trying to use machine learning to predict a dataset. It is a regression problem with 180 input features and 1 continuously-valued output. I try to compare deep neural networks, random forest regression, and linear regression.
As I expect, 3-hidden-layer deep neural networks outperform other two approaches with a root mean square error (RMSE) of 0.1. However, I unexpected to see that random forest even performs worse than linear regression (RMSE 0.29 vs. 0.27). In my expectation, the random forest can discover more complex dependencies between features to decrease error. I have tried to tune the parameters of random forest (number of trees, maximum features, max_depth, etc.). I also tried different K-cross validation, but the performance is still less than linear regression.
I searched online, and one answer says linear regression may perform better if features have a smooth, nearly linear dependence on the covariates. I do not fully get the point because if that is the case, should not deep neural networks give much performance gain?
I am struggling to give an explanation. Under what situation, random forest is worse than linear regression, but deep neural networks can perform much better?
If your features explain linear relation to the target variable then a Linear Model usually performs well than a Random Forest Model. It totally depends on the linear relations between your features.
That said, Linear models are not superior or the Random Forest is any inferior one.
Try scaling and transforming the data using MinMaxScaler() from scikit-learn to see if the linear model improves further
Pro Tips
If linear model is working like a charm you need to ask your self Why? and How? And get into the basics of both the models to understand why it worked on your data. These questions will lead you to feature engineer better. And as a matter of fact, Kaggle Grand Masters do use Linear Models in stacking to get that top 1% score by capturing the linear relations in the dataset.
So at the end of the day, linear models could wonders too.
According to my understanding, RF selects features randomly and hence is hard to overfit. But, in sklearn Gradient boosting also offers the option of max_features which can help to prevent overfitting. So, why would anyone use Random forest?
Can anyone explain when to use Gradient boosting vs Random forest based on the given data?
Any help is highly appreciated.
According to my personal experience, Random Forest could be a better choice when..
You train a model on small data set.
Your data set has few features to learn.
Your data set has low Y flag count or you try to predict a situation that has low chance to occur or rarely occurs.
In these situations, Gradient Boosting algorithms like XGBoost and Light GBM can overfit (though their parameters are tuned) while simple algorithms like Random Forest or even Logistic Regression may perform better. To illustrate, for XGboost and Ligh GBM, ROC AUC from test set may be higher in comparison with Random Forest but shows too high difference with ROC AUC from train set.
Despite the sharp prediction form Gradient Boosting algorithms, in some cases, Random Forest take advantage of model stability from begging methodology (selecting randomly) and outperform XGBoost and Light GBM. However, Gradient Boosting algorithms perform better in general situations.
Similar question asked on Quora:
https://www.quora.com/How-do-random-forests-and-boosted-decision-trees-compare
I agree with the author at the link that random forests are more robust -- they don't require much problem-specific tuning to get good results. Besides that, a couple other items based on my own experience:
Random forests can perform better on small data sets; gradient boosted trees are data hungry
Random forests are easier to explain and understand. This perhaps seems silly but can lead to better adoption of a model if needed to be used by less technical people
I think that's also true. I have also read on this page How Random Forest Works
There explains the advantages of random forest. like this :
For applications in classification problems, Random Forest algorithm
will avoid the overfitting problem
For both classification and
regression task, the same random forest algorithm can be used
The Random Forest algorithm can be used for identifying the most
important features from the training dataset, in other words,
feature engineering.
Regarding classification...
Suppose that it is found a data to be linearly separable( tested the linear separability using SVM/Clustering/Single perceptron etc..)
Can we go with a simpler model like logistic regression (instead of SVM or any other) as they say simple model is the better model
Please correct me if wrong
Thanks in advance !
Surya
Don't confuse the algorithm with the model. With linearly separable data, each of those algorithms should return a simple hyperplane, a sum of linear (first-degree) terms with real coefficients. Thus, each of the models is equally simple.
If you're concerned with the simplest algorithm, then you do have a point.
I would stick with straightforward SVM: it provides a closed-form computation to determine the optimum separation, based on the nearest N+1 observations (given N features).
Each of the algorithms has its advantages with respect to run-time, clarity, accuracy, etc. If your criterion is something other than maximum gap, then linear regression (in its closed form) may be the best choice.
My colleague and I are trying to wrap our heads around the difference between logistic regression and an SVM. Clearly they are optimizing different objective functions. Is an SVM as simple as saying it's a discriminative classifier that simply optimizes the hinge loss? Or is it more complex than that? How do the support vectors come into play? What about the slack variables? Why can't you have deep SVM's the way you can't you have a deep neural network with sigmoid activation functions?
I will answer one thing at at time
Is an SVM as simple as saying it's a discriminative classifier that simply optimizes the hinge loss?
SVM is simply a linear classifier, optimizing hinge loss with L2 regularization.
Or is it more complex than that?
No, it is "just" that, however there are different ways of looking at this model leading to complex, interesting conclusions. In particular, this specific choice of loss function leads to extremely efficient kernelization, which is not true for log loss (logistic regression) nor mse (linear regression). Furthermore you can show very important theoretical properties, such as those related to Vapnik-Chervonenkis dimension reduction leading to smaller chance of overfitting.
Intuitively look at these three common losses:
hinge: max(0, 1-py)
log: y log p
mse: (p-y)^2
Only the first one has the property that once something is classified correctly - it has 0 penalty. All the remaining ones still penalize your linear model even if it classifies samples correctly. Why? Because they are more related to regression than classification they want a perfect prediction, not just correct.
How do the support vectors come into play?
Support vectors are simply samples placed near the decision boundary (losely speaking). For linear case it does not change much, but as most of the power of SVM lies in its kernelization - there SVs are extremely important. Once you introduce kernel, due to hinge loss, SVM solution can be obtained efficiently, and support vectors are the only samples remembered from the training set, thus building a non-linear decision boundary with the subset of the training data.
What about the slack variables?
This is just another definition of the hinge loss, more usefull when you want to kernelize the solution and show the convexivity.
Why can't you have deep SVM's the way you can't you have a deep neural network with sigmoid activation functions?
You can, however as SVM is not a probabilistic model, its training might be a bit tricky. Furthermore whole strength of SVM comes from efficiency and global solution, both would be lost once you create a deep network. However there are such models, in particular SVM (with squared hinge loss) is nowadays often choice for the topmost layer of deep networks - thus the whole optimization is actually a deep SVM. Adding more layers in between has nothing to do with SVM or other cost - they are defined completely by their activations, and you can for example use RBF activation function, simply it has been shown numerous times that it leads to weak models (to local features are detected).
To sum up:
there are deep SVMs, simply this is a typical deep neural network with SVM layer on top.
there is no such thing as putting SVM layer "in the middle", as the training criterion is actually only applied to the output of the network.
using of "typical" SVM kernels as activation functions is not popular in deep networks due to their locality (as opposed to very global relu or sigmoid)
Most classification algorithms are developed to improve the training speed. However, is there any classifier or algorithm focusing on the decision making speed(low computation complexity and simple realizable structure)? I can get enough training dataļ¼and endure the long training time.
There are many methods which classify fast, you could more or less sort models by classification speed in a following way (first ones - the fastest, last- slowest)
Decision Tree (especially with limited depth)
Linear models (linear regression, logistic regression, linear svm, lda, ...) and Naive Bayes
Non-linear models based on explicit data transformation (Nystroem kernel approximation, RVFL, RBFNN, EEM), Kernel methods (such as kernel SVM) and shallow neural networks
Random Forest and other committees
Big Neural Networks (ie. CNN)
KNN with arbitrary distance
Obviously this list is not exhaustive, it just shows some general ideas.
One way of obtaining such model is to build a complex, slow model, then use it as a black box label generator to train a simplier model (but on potentialy infinite training set) - thus getting a fast classifier at the cost of very expensive training. There are many works showing that one can do that for example by training a shallow neural network on outputs of deep nn.
In general classification speed should not be a problem. Some exceptions are algorithms which have a time complexity depending on the number of samples you have for training. One example is k-Nearest-Neighbors which has no training time, but for classification it needs to check all points (if implemented in a naive way). Other examples are all classifiers which work with kernels since they compute the kernel between the current sample and all training samples.
Many classifiers work with a scalar product of the features and a learned coefficient vector. These should be fast enough in almost all cases. Examples are: Logistic regression, linear SVM, perceptrons and many more. See #lejlot's answer for a nice list.
If these are still too slow you might try to reduce the dimension of your feature space first and then try again (this also speeds up training time).
Btw, this question might not be suited for StackOverflow as it is quite broad and recommendation instead of problem oriented. Maybe try https://stats.stackexchange.com/ next time.
I have a decision tree which is represented in the compressed form and which is at least 4 times faster than the actual tree in classifying an unseen instance.