randomUniformForest (version 1.1.6)

randomUniformForest-package: Random Uniform Forests for Classification, Regression and Unsupervised Learning

Description

Ensemble model for classification, regression and unsupervised learning, based on a forest of unpruned and randomized binary decision trees. Unlike Breiman's Random Forests, each tree is grown by sampling, with replacement, a set of variables before splitting each node. Each cut-point is generated randomly, according to the continuous Uniform distribution between two random points of each candidate variable or using its whole current support. Optimal random node is, then, selected among many full random ones by maximizing Information Gain (classification) or minimizing a distance (regression), 'L2' (or 'L1'). Unlike Extremely Randomized Trees, data are either bootstrapped or sub-sampled for each tree. From the theoretical side, Random Uniform Forests are aimed to lower correlation between trees and to offer a deep analysis of variable importance. The unsupervised mode introduces clustering and dimension reduction, using a three-layer engine: dissimilarity matrix, Multidimensional Scaling (or spectral decomposition) and k-means (or hierarchical clustering). From the practical side, Random Uniform Forests are designed to provide a complete analysis of (un)supervised problems and to allow native distributed and incremental learning.

Details

Package:	randomUniformForest
Type:	Package
Version:	1.1.5
Date:	2015-02-16
License:	BSD_3_clause

Installation: install.packages("randomUniformForest") Usage: library(randomUniformForest)

References

Amit, Y., Geman, D., 1997. Shape Quantization and Recognition with Randomized Trees. Neural Computation 9, 1545-1588.

Biau, G., Devroye, L., Lugosi, G., 2008. Consistency of random forests and other averaging classifiers. The Journal of Machine Learning Research 9, 2015-2033.

Bousquet, O., Boucheron, S., Lugosi, G., 2004. Introduction to Statistical Learning Theory, in: Bousquet, O., Luxburg, U. von, Ratsch, G. (Eds.), Advanced Lectures on Machine Learning, Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp. 169-207.

Breiman, L, 1996. Heuristics of instability and stabilization in model selection. The Annals of Statistics 24, no. 6, 2350-2383.

Breiman, L., 1996. Bagging predictors. Machine learning 24, 123-140.

Breiman, L., 2001. Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author). Statistical Science 16, no. 3, 199-231.

Breiman, L., 2001. Random Forests, Machine Learning 45(1), 5-32.

Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C., 1984. Classification and Regression Trees. New York: Chapman and Hall.

Ciss, S., 2014. PhD thesis: Forets uniformement aleatoires et detection des irregularites aux cotisations sociales. Universite Paris Ouest Nanterre, France. In french. English title : Random Uniform Forests and Irregularity Detection in social Security contributions. Link : https://www.dropbox.com/s/q7hbgeafrdd8qtc/Saip_Ciss_These.pdf?dl=0

Ciss, S., 2015a. Random Uniform Forests. Preprint. hal-01104340.

Ciss, S., 2015b. Variable Importance in Random Uniform Forests. Preprint. hal-01104751.

Ciss, S., 2015c. Generalization Error and Out-of-bag Bounds in Random (Uniform) Forests. Preprint. hal-01110524.

Cox, T. F., Cox, M. A. A., 2001. Multidimensional Scaling. Second edition. Chapman and Hall.

Devroye, L., Gyorfi, L., Lugosi, G., 1996. A probabilistic theory of pattern recognition. New York: Springer.

Dietterich, T.G., 2000. Ensemble Methods in Machine Learning, in : Multiple Classifier Systems, Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp. 1-15.

Efron, B., 1979. Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics 7, 1-26.

Gower, J. C., 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53, 325-328.

Gyorfi, L., 2002. A distribution-free theory of nonparametric regression. Springer Science & Business Media.

Hastie, T., Tibshirani, R., Friedman, J.J.H., 2001. The elements of statistical learning. New York: Springer.

Ho, T.K., 1998. The random subspace method for constructing decision forests. IEEE Transactions on Pattern Analysis and Machine Intelligence 20, 832-844.

Lin, Y., Jeon, Y., 2002. Random Forests and Adaptive Nearest Neighbors. Journal of the American Statistical Association 101-474.

Ng, A. Y., Jordan, M. I., Weiss, Y., 2002. On spectral clustering: Analysis and an algorithm. Advances in neural information processing systems, 2, 849-856.

Vapnik, V.N., 1995. The nature of statistical learning theory. Springer-Verlag New York, Inc., New York, NY, USA.

Examples

# NOT RUN {
## Presenting some of the core functions
## Not run

## 1 - Classification: iris data set (assess whole data)

## load data (included in R):
# data(iris)
# XY = iris
# p = ncol(XY)
# X = XY[,-p]
# Y = XY[,p]

## Train a model : using formula
# iris.ruf = randomUniformForest(Species ~., XY, threads = 1)

## or using matrix
## iris.ruf = randomUniformForest(X, as.factor(Y), threads = 1)

## Assess model : Out-of-bag (OOB) evaluation
# iris.ruf

## Variable Importance : base assessment
# summary(iris.ruf)

## Variable Importance : deeper assessment (explain the modelling)
# iris.importance = importance(iris.ruf, Xtest = X, maxInteractions = p - 1)

## Visualize : details of Variable Importance 
## (tile windows vertically, using the R menu, to see all plots)
# plot(iris.importance, Xtest = X)

## Analyse : get an interpretation of the model results
# iris.ruf.analysis = clusterAnalysis(iris.importance, X, components = 3, 
# clusteredObject = iris.ruf, OOB = TRUE)

## Dimension reduction, clustering and visualization : OOB evaluation
# iris.clust.ruf = clusteringObservations(iris.ruf, X, importanceObject = iris.importance)

## 2 - Regression: Boston Housing (assess a test set)

## load data :
# install.packages("mlbench") ##if not installed
# data(BostonHousing, package = "mlbench")

# XY = BostonHousing
# p = ncol(XY)
# X = XY[,-p]
# Y = XY[,p]

## get random training and test sets :
## reproducibility :
# set.seed(2015)

# train_test = init_values(X, Y, sample.size = 1/2)
# Xtrain = train_test$xtrain
# Ytrain = train_test$ytrain
# Xtest = train_test$xtest
# Ytest = train_test$ytest

## Train a model : 
# boston.ruf = randomUniformForest(Xtrain, Ytrain)

## Assess (quickly) the model : 
# boston.ruf
# plot(boston.ruf)
# summary(boston.ruf)

## Predict the test set :
# boston.pred.ruf = predict(boston.ruf, Xtest)

## or predict quantiles
# boston.predQunatile_97.5.ruf = predict(boston.ruf, Xtest, type = "quantile", 
# whichQuantile = 0.975)

## or prediction intervals
# boston.predConfInt_95.ruf = predict(boston.ruf, Xtest, type = "confInt", conf = 0.95)

## Assess predictions :
# statsModel = model.stats(boston.pred.ruf, Ytest, regression = TRUE)

## Avoiding overfitting : under the i.i.d. assumption, OOB error
## is expected to be an upper bound of MSE. Convergence is first needed.
## Convergence needs low correlation between trees residuals.

# boston.ruf

## The easy way; reduce correlation(decreasing 'mtry' value) + post-processing 
# bostonNew.ruf = randomUniformForest(Xtrain, Ytrain, mtry = 4)

## (predict and) Post-process :
# bostonNew.predAll.ruf = predict(bostonNew.ruf, Xtest, type = "all")

# bostonNew.postProcessPred.ruf = postProcessingVotes(bostonNew.ruf, 
# predObject = bostonNew.predAll.ruf)

## Assess new predictions :
# statsModel = model.stats(bostonNew.postProcessPred.ruf, Ytest, regression = TRUE)

## Convergence : grow more trees
# bostonNew.moreTrees.ruf = rUniformForest.grow(bostonNew.ruf, Xtrain, ntree = 100)
# }