# Alternatives to classification trees, with better predictive (e.g: CV) performance?

I am looking for an alternative to Classification Trees which might yield better predictive power.

The data I am dealing with has factors for both the explanatory and the explained variables.

I remember coming across random forests and neural networks in this context, although never tried them before, are there another good candidate for such a modeling task (in R, obviously)?

• Don't bother with neural networks, this is an obsolete technology. – user88 Oct 10 '10 at 13:22
• @mbq do you still stand by this statement? – rhombidodecahedron May 7 '18 at 12:04
• @rhombidodecahedron Sure, play with NNs from 2010 and you'll agree. Besides, I doubt that any DL model would bring anything to a table with data of (presumably) such small size. – user88 May 23 '18 at 15:56

I think it would be worth giving a try to Random Forests (randomForest); some references were provided in response to related questions: Feature selection for “final” model when performing cross-validation in machine learning; Can CART models be made robust?. Boosting/bagging render them more stable than a single CART which is known to be very sensitive to small perturbations. Some authors argued that it performed as well as penalized SVM or Gradient Boosting Machines (see, e.g. Cutler et al., 2009). I think they certainly outperform NNs.

Boulesteix and Strobl provides a nice overview of several classifiers in Optimal classifier selection and negative bias in error rate estimation: an empirical study on high-dimensional prediction (BMC MRM 2009 9: 85). I've heard of another good study at the IV EAM meeting, which should be under review in Statistics in Medicine,

João Maroco, Dina Silva, Manuela Guerreiro, Alexandre de Mendonça. Do Random Forests Outperform Neural Networks, Support Vector Machines and Discriminant Analysis classifiers? A case study in the evolution to dementia in elderly patients with cognitive complaints

I also like the caret package: it is well documented and allows to compare predictive accuracy of different classifiers on the same data set. It takes care of managing training /test samples, computing accuracy, etc in few user-friendly functions.

The glmnet package, from Friedman and coll., implements penalized GLM (see the review in the Journal of Statistical Software), so you remain in a well-known modeling framework.

Otherwise, you can also look for association rules based classifiers (see the CRAN Task View on Machine Learning or the Top 10 algorithms in data mining for a gentle introduction to some of them).

I'd like to mention another interesting approach that I plan to re-implement in R (actually, it's Matlab code) which is Discriminant Correspondence Analysis from Hervé Abdi. Although initially developed to cope with small-sample studies with a lot of explanatory variables (eventually grouped into coherent blocks), it seems to efficiently combine classical DA with data reduction techniques.

References

1. Cutler, A., Cutler, D.R., and Stevens, J.R. (2009). Tree-Based Methods, in High-Dimensional Data Analysis in Cancer Research, Li, X. and Xu, R. (eds.), pp. 83-101, Springer.
2. Saeys, Y., Inza, I., and Larrañaga, P. (2007). A review of feature selection techniques in bioinformatics. Bioinformatics, 23(19): 2507-2517.
• +1 Great answer. I also agree with the caret recommendation. – Shane Oct 10 '10 at 21:00

It's important to bear in mind that there's no one algorithm that's always better than others. As stated by Wolpert and Macready, "any two algorithms are equivalent when their performance is averaged across all possible problems." (See Wikipedia for details.)

For a given application, the "best" one is generally one that is most closely aligned to your application in terms of the assumptions it makes, the kinds of data it can handle, the hypotheses it can represent, and so on.

So it's a good idea to characterise your data according to criteria such as:

• Do I have a very large data set or a modest one?
• Is the dimensionality high?
• Are variables numerical (continuous/discrete) or symbolic, or a mix, and/or can they be transformed if necessary?
• Are variables likely to be largely independent or quite dependent?
• Are there likely to be redundant, noisy, or irrelevant variables?
• Do I want to be able to inspect the model generated and try to make sense of it?

By answering these, you can eliminate some algorithms and identify others as potentially relevant, and then maybe end up with a small set of candidate methods that you have intelligently chosen as likely to be useful.

Sorry not to give you a simple answer, but I hope this helps nonetheless!

• +1 Love the quote. ("any two algorithms are equivalent when their performance is averaged across all possible problems.") – Assad Ebrahim Jan 15 '13 at 15:31

For multi-class classification, support vector machines are also a good choice. I typically use the the R kernlab package for this.

See the following JSS paper for a good discussion: http://www.jstatsoft.org/v15/i09/

• @Tal Here is a fair (or I think so) review of SVM vs. RFs: A comprehensive comparison of random forests and support vector machines for microarray-based cancer classification, j.mp/ab7U8V. I also prefer kernlab to e1071. – chl Oct 10 '10 at 19:25
• @chl I don't like this paper while it made from the SVM learning perspective -- making one repetition of a stochastic algorithm (RF) is just a junk; also appendix 2 shows how bad it may be to apply SVM workflow to RF. Yet I agree that almost always SVM can be tuned to outperform RF because of the kernel trick (which plain RF does not have, while it doesn't mean it can't have it in general), but with exponentially growing optimization effort. – user88 Oct 12 '10 at 12:13
• @mbq Indeed, this a good point. – chl Oct 12 '10 at 13:03

As already mentioned Random Forests are a natural "upgrade" and, these days, SVM are generally the recommended technique to use.

I want to add that more often than not switching to SVM yields very disappointing results. Thing is, whilst techniques like random trees are almost trivial to use, SVM are a bit trickier.

I found this paper invaluable back when I used SVM for the first time (A Practical Guide to Support Vector Classication) http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf

In R you can use the the e1071 package for SVM, it links against the de facto standard (in free software at least!) libSVM library.

• kernlab also uses libsvm for the optimization, so there isn't a big difference in that sense (although it is much more flexible). – Shane Oct 10 '10 at 16:44

Its worth to take a look at Naive Bayes classifiers. In R you can perform Naive Bayes classification in the packages e1071 and klaR.