Random forest

Random forest (or random forests) is an ensemble classifier that consists of many decision trees and outputs the class that is the mode of the class's output by individual trees. The algorithm for inducing a random forest was developed by Leo Breiman^[1] and Adele Cutler, and "Random Forests" is their trademark. The term came from random decision forests that was first proposed by Tin Kam Ho of Bell Labs in 1995. The method combines Breiman's "bagging" idea and the random selection of features, introduced independently by Ho^[2]^[3] and Amit and Geman^[4] in order to construct a collection of decision trees with controlled variation.

The selection of a random subset of features is an example of the random subspace method, which, in Ho's formulation, is a way to implement stochastic discrimination^[5] proposed by Eugene Kleinberg.

1 Learning algorithm
2 Features and Advantages
3 Disadvantages
4 Visualization
5 See also
6 References
7 Commercial implementation
8 Open source implementations
9 External links

Learning algorithm

Each tree is constructed using the following algorithm:

Let the number of training cases be N, and the number of variables in the classifier be M.
We are told the number m of input variables to be used to determine the decision at a node of the tree; m should be much less than M.
Choose a training set for this tree by choosing n times with replacement from all N available training cases (i.e. take a bootstrap sample). Use the rest of the cases to estimate the error of the tree, by predicting their classes.
For each node of the tree, randomly choose m variables on which to base the decision at that node. Calculate the best split based on these m variables in the training set.
Each tree is fully grown and not pruned (as may be done in constructing a normal tree classifier).

For prediction a new sample is pushed down the tree. It is assigned the label of the training sample in the terminal node it ends up in. This procedure is iterated over all trees in the ensemble, and the average vote of all trees is reported as random forest prediction.

Features and Advantages

The advantages of random forest are:

It is one of the most accurate learning algorithms available. For many data sets, it produces a highly accurate classifier.^[6]
It runs efficiently on large databases.
It can handle thousands of input variables without variable deletion.
It gives estimates of what variables are important in the classification.
It generates an internal unbiased estimate of the generalization error as the forest building progresses.
It has an effective method for estimating missing data and maintains accuracy when a large proportion of the data are missing.
It has methods for balancing error in class population unbalanced data sets.
Generated forests can be saved for future use on other data.
Prototypes are computed that give information about the relation between the variables and the classification.
It computes proximities between pairs of cases that can be used in clustering, locating outliers, or (by scaling) give interesting views of the data.
The capabilities of the above can be extended to unlabeled data, leading to unsupervised clustering, data views and outlier detection.
It offers an experimental method for detecting variable interactions.

Disadvantages

Random forests have been observed to overfit for some datasets with noisy classification/regression tasks.^[7]
For data including categorical variables with different number of levels, random forests are biased in favor of those attributes with more levels. Therefore, the variable importance scores from random forest are not reliable for this type of data.^[8]

Visualization

In order to form an intuitive visualization of the model-space represented by a random forest, a dataset consisting of 200 random points (100 green points and 100 red points) was created. The green points were drawn from a Gaussian distribution with a centroid at (0,1), and the red points were drawn from a Gaussian distribution with a centroid at (1,0). In both cases, the variance was circular with an average radius of 1.

A Random Forest model, consisting of 50 trees, was trained on this data. The purity of the color indicates the portion of the 50 trees that voted in agreement. Significant over-fit can be observed in this visualization.

For contrast, a logistic regression model (which is somewhat less-prone to over-fit) was also trained on this same data.

(Typically, random forest is best-suited for use with categorical features, but continuous features were used in this illustration because they were easier to visualize.)

References

^ Breiman, Leo (2001). "Random Forests". Machine Learning 45 (1): 5–32. doi:10.1023/A:1010933404324.
^ Ho, Tin (1995). "Random Decision Forest". 3rd Int'l Conf. on Document Analysis and Recognition. pp. 278–282. http://cm.bell-labs.com/cm/cs/who/tkh/papers/odt.pdf.
^ Ho, Tin (1998). "The Random Subspace Method for Constructing Decision Forests". IEEE Transactions on Pattern Analysis and Machine Intelligence 20 (8): 832–844. doi:10.1109/34.709601. http://cm.bell-labs.com/cm/cs/who/tkh/papers/df.pdf.
^ Amit, Y.; Geman, D. (1997). "Shape quantization and recognition with randomized trees". Neural Computation 9 (7): 1545–1588. doi:10.1162/neco.1997.9.7.1545. http://www.cis.jhu.edu/publications/papers_in_database/GEMAN/shape.pdf.
^ Kleinberg, Eugene (1996). "An Overtraining-Resistant Stochastic Modeling Method for Pattern Recognition". Annals of Statistics 24 (6): 2319–2349. doi:10.1214/aos/1032181157. MR 1425956. http://kappa.math.buffalo.edu/aos.pdf.
^ Caruana, Rich; Karampatziakis, Nikos; Yessenalina, Ainur (2008). "An empirical evaluation of supervised learning in high dimensions". Proceedings of the 25th International Conference on Machine Learning (ICML). http://icml2008.cs.helsinki.fi/papers/632.pdf.
^ Segal, Mark R. (April 14 2004). Machine Learning Benchmarks and Random Forest Regression. Center for Bioinformatics & Molecular Biostatistics. http://repositories.cdlib.org/cbmb/bench_rf_regn/.
^ Deng,H.; Runger, G.; Tuv, E. (2011). "Bias of importance measures for multi-valued attributes and solutions". Proceedings of the 21st International Conference on Artificial Neural Networks (ICANN). http://enpub.fulton.asu.edu/hdeng3/MultiICANN2011.pdf.

Commercial implementation

[1] Random Forests.

Open source implementations

The Original RF by Breiman and Cutler. Written in Fortran 77. May be difficult to configure. GNU General Public License
ALGLIB contains an implementation of a modified random forest algorithm in C#, C++, Pascal, VBA. GPL 2+
orngEnsemble module within Orange data mining software suite. licenses
PARF Written in Fortran 90. Can distribute work over a cluster of computers using MPI.
party An implementation of Breiman's random forest based on conditional inference trees for R.
randomForest for R.
Oblique random forests for R based on multivariate decision trees.
TMVA Toolkit for Multivariate Data Analysis implements random forests.
milk for Python implements random forests.
[2] Matlab version. GNU GPL v2
Nimbus A Ruby gem implementing random forest for genomic selection contexts.
Apache Mahout. Apache license
Stochastic Bosque A Matlab implementation.
The Waffles machine learning toolkit includes an implementation of random forest.
RF-ACE uses Random Forests for feature filtering and Gradient Boosting Trees for data prediction. Written in C++. Apache License 2.0.

External links

Random Forests classifier description (Site of Leo Breiman)
Liaw, Andy & Wiener, Matthew "Classification and Regression by randomForest" R News (2002) Vol. 2/3 p. 18 (Discussion of the use of the random forest package for R)
Ho, Tin Kam (2002). "A Data Complexity Analysis of Comparative Advantages of Decision Forest Constructors". Pattern Analysis and Applications 5, p. 102-112 (Comparison of bagging and random subspace method)
Prinzie, Anita; Poel, Dirk (2007). "Random Multiclass Classification: Generalizing Random Forests to Random MNL and Random NB". Database and Expert Systems Applications. Lecture Notes in Computer Science. 4653. pp. 349. doi:10.1007/978-3-540-74469-6_35. ISBN 978-3-540-74467-2.
Prinzie, Anita; Van Den Poel, Dirk (2008). "Random Forests for multiclass classification: Random MultiNomial Logit". Expert Systems with Applications 34 (3): 1721. doi:10.1016/j.eswa.2007.01.029.