imbalanced.rfsrc: Imbalanced Two Class Problems

Description

Implements various solutions to the two-class imbalanced problem, including the newly proposed quantile-classifier approach of O'Brien and Ishwaran (2017). Also includes Breiman's balanced random forests undersampling of the majority class. Performance is assesssed using the G-mean, but misclassification error can be requested.

Usage

# S3 method for rfsrc
imbalanced(formula, data, ntree = 3000, 
  method = c("rfq", "brf", "standard"),
  block.size = NULL, perf.type = NULL, fast = FALSE,
  ratio = NULL, optimize = FALSE, ngrid = 1e4,
  ...)

Arguments

formula

A symbolic description of the model to be fit.

data

Data frame containing the two-class y-outcome and x-variables.

ntree

Number of trees.

method

Method used for fitting the classifier. The default is rfq which is the random forests quantile-classifer (RFQ) approach of O'Brien and Ishwaran (2017). The method brf implements the balanced random forest (BRF) method of Chen et al. (2004) which undersamples the majority class so that its cardinality matches that of the minority class. The method standard implements a standard random forest analysis.

perf.type

Measure used for assessing performance (and all downstream calculations based on it such as variable importance). The default for rfq and brf is to use the G-mean (Kubat et al., 1997). For standard random forests, the default is misclassification error. Users can over-ride the default performance measure by manually selecting either g.mean for the G-mean, misclass for misclassification error, or brier for the normalized Brier score. See the examples below.

block.size

Should the cumulative error rate be calculated on every tree? When NULL, it will only be calculated on the last tree. If importance is requested, VIMP is calculated in "blocks" of size equal to block.size.

fast

Use fast random forests, rfsrc.fast, in place of rfsrc? Improves speed but is less accurate. Only applies to RFQ.

ratio

This is an optional parameter for expert users and included only for experimental purposes. Used to specify the ratio (between 0 and 1) for undersampling the majority class. Sampling is without replacement. Option is ignored for BRF.

optimize

Calculate the G-mean under various threshold values? Returns out-of-bag G-mean values for each tested threshold value. See examples below for illustration.

ngrid

Number of threshold values attempted when optimize is requested

...

Further arguments to be passed to the rfsrc function to specify random forest parameters.

Value

A two-class random forest fit under the requested method and performance value.

Details

Imbalanced data, or the so-called imbalanced minority class problem, refers to classification settings involving two-classes where the ratio of the majority class to the minority class is much larger than one. Two solutions to the two-class imbalanced problem are provided here, including the newly proposed random forests quantile-classifier (RFQ) of O'Brien and Ishwaran (2017), and the balanced random forests (BRF) undersampling approach of Chen et al. (2004). The default performance metric is the G-mean (Kubat et al., 1997).

Currently, missing values cannot be handled for BRF or when the ratio option is used; in these cases, missing data is removed prior to the analysis.

We recommend setting ntree to a relatively large value when dealing with imbalanced data to ensure convergence of the performance value -- this is especially true for the G-mean. Consider using 5 times the usual number of trees.

References

Chen, C., Liaw, A. and Breiman, L. (2004). Using random forest to learn imbalanced data. University of California, Berkeley, Technical Report 110.

Kubat, M., Holte, R. and Matwin, S. (1997). Learning when negative examples abound. Machine Learning, ECML-97: 146-153.

O'Brien R. and Ishwaran H. (2019). A random forests quantile classifier for class imbalanced data. Pattern Recognition, 90, 232-249

Examples

Run this code

# NOT RUN {
## ------------------------------------------------------------
## use the breast data for illustration
## ------------------------------------------------------------

data(breast, package = "randomForestSRC")
breast <- na.omit(breast)
f <- as.formula(status ~ .)

##----------------------------------------------------------------
## default RFQ call
##----------------------------------------------------------------

o.rfq <- imbalanced(f, breast)
print(o.rfq)

## equivalent to:
## rfsrc(f, breast, rfq =  TRUE, ntree = 3000, perf.type = "g.mean") 

##----------------------------------------------------------------
## detailed output using customized performance function
##----------------------------------------------------------------

print(get.imbalanced.performance(o.rfq))

##----------------------------------------------------------------
## RFQ with AUC splitting
##----------------------------------------------------------------

print(o.rfq <- imbalanced(f, breast, splitrule = "auc"))
print(get.imbalanced.performance(o.rfq))

##----------------------------------------------------------------
## RFQ call with fast rfsrc
##----------------------------------------------------------------

o.rfq <- imbalanced(f, breast, fast = TRUE)
print(o.rfq)

## equivalent to:
## rfsrc.fast(f, breast, ntree = 3000, rfq =  TRUE, perf.type = "g.mean") 

##-----------------------------------------------------------------
## standard RF (uses misclassification)
## ------------------------------------------------------------

o.std <- imbalanced(f, breast, method = "stand")

##-----------------------------------------------------------------
## standard RF using G-mean performance
## ------------------------------------------------------------

o.std <- imbalanced(f, breast, method = "stand", perf.type = "g.mean")

## equivalent to:
## rfsrc(f, breast, ntree = 3000, perf.type = "g.mean")

##----------------------------------------------------------------
## default BRF call 
##----------------------------------------------------------------

o.brf <- imbalanced(f, breast, method = "brf")

## equivalent to:
## imbalanced(f, breast, method = "brf", perf.type = "g.mean")

##----------------------------------------------------------------
## BRF call with misclassification performance 
##----------------------------------------------------------------

o.brf <- imbalanced(f, breast, method = "brf", perf.type = "misclass")

##----------------------------------------------------------------
## RFQ with optimized threshold
##----------------------------------------------------------------

o.rfq.opt <- imbalanced(f, breast, optimize = TRUE)
plot(o.rfq.opt$gmean, type = "l")

##----------------------------------------------------------------
## train/test example
##----------------------------------------------------------------

trn <- sample(1:nrow(breast), size = nrow(breast) / 2)
o.trn <- imbalanced(f, breast[trn,], importance = TRUE)
o.tst <- predict(o.trn, breast[-trn,], importance = TRUE)
print(o.trn)
print(o.tst)
print(100 * cbind(o.trn$impo[, 1], o.tst$impo[, 1]))

##----------------------------------------------------------------
## simulation example using the caret R-package
## creates imbalanced data by randomly sampling the class 1 data
##
## uses SMOTE from "imbalance" package to oversample the minority
## illustrates RFQ with and without SMOTE
##
##----------------------------------------------------------------

if (library("caret", logical.return = TRUE) &
    library("imbalance", logical.return = TRUE)) {

  ## experimental settings
  n <- 5000
  q <- 20
  ir <- 6
  f <- as.formula(Class ~ .)
 
  ## simulate the data, create minority class data
  d <- twoClassSim(n, linearVars = 15, noiseVars = q)
  d$Class <- factor(as.numeric(d$Class) - 1)
  idx.0 <- which(d$Class == 0)
  idx.1 <- sample(which(d$Class == 1), sum(d$Class == 1) / ir , replace = FALSE)
  d <- d[c(idx.0,idx.1),, drop = FALSE]
  d <- d[sample(1:nrow(d)), ]

  ## define train/test split
  trn <- sample(1:nrow(d), size = nrow(d) / 2, replace = FALSE)

  ## now make SMOTE training data
  newd.50 <- mwmote(d[trn, ], numInstances = 50, classAttr = "Class")
  newd.500 <- mwmote(d[trn, ], numInstances = 500, classAttr = "Class")

  ## fit RFQ with and without SMOTE
  o.with.50 <- imbalanced(f, rbind(d[trn, ], newd.50)) 
  o.with.500 <- imbalanced(f, rbind(d[trn, ], newd.500))
  o.without <- imbalanced(f, d[trn, ])
  
  ## compare performance on test data
  print(predict(o.with.50, d[-trn, ]))
  print(predict(o.with.500, d[-trn, ]))
  print(predict(o.without, d[-trn, ]))
  
}

##----------------------------------------------------------------
## simulation example using the caret R-package similar to above
##
## illustrates effectiveness of blocked VIMP
##
##----------------------------------------------------------------

if (library("caret", logical.return = TRUE)) {

  ## experimental settings
  n <- 1000
  q <- 20
  ir <- 6
  f <- as.formula(Class ~ .)
 
  ## simulate the data, create minority class data
  d <- twoClassSim(n, linearVars = 15, noiseVars = q)
  d$Class <- factor(as.numeric(d$Class) - 1)
  idx.0 <- which(d$Class == 0)
  idx.1 <- sample(which(d$Class == 1), sum(d$Class == 1) / ir , replace = FALSE)
  d <- d[c(idx.0,idx.1),, drop = FALSE]

  ## VIMP for BRF with and without blocking
  ## blocked VIMP is a hybrid of Breiman-Cutler/Ishwaran-Kogalur VIMP
  brf <- imbalanced(f, d, method = "brf", importance = TRUE, block.size = 1)
  brfB <- imbalanced(f, d, method = "brf", importance = TRUE, block.size = 10)

  ## VIMP for RFQ with and without blocking
  rfq <- imbalanced(f, d, importance = TRUE, block.size = 1)
  rfqB <- imbalanced(f, d, importance = TRUE, block.size = 10)

  ## compare VIMP values
  imp <- 100 * cbind(brf$importance[, 1], brfB$importance[, 1],
                     rfq$importance[, 1], rfqB$importance[, 1])
  legn <- c("BRF", "BRF-block", "RFQ", "RFQ-block")
  colr <- rep(4,20+q)
  colr[1:20] <- 2
  ylim <- range(c(imp))
  nms <- 1:(20+q)
  par(mfrow=c(2,2))
  barplot(imp[,1],col=colr,las=2,main=legn[1],ylim=ylim,names.arg=nms)
  barplot(imp[,2],col=colr,las=2,main=legn[2],ylim=ylim,names.arg=nms)
  barplot(imp[,3],col=colr,las=2,main=legn[3],ylim=ylim,names.arg=nms)
  barplot(imp[,4],col=colr,las=2,main=legn[4],ylim=ylim,names.arg=nms)

}

##----------------------------------------------------------------
##
## confidence intervals for G-mean VIMP using subsampling
##
##----------------------------------------------------------------

if (library("caret", logical.return = TRUE)) {

  ## experimental settings
  n <- 1000
  q <- 20
  ir <- 6
  f <- as.formula(Class ~ .)
 
  ## simulate the data, create minority class data
  d <- twoClassSim(n, linearVars = 15, noiseVars = q)
  d$Class <- factor(as.numeric(d$Class) - 1)
  idx.0 <- which(d$Class == 0)
  idx.1 <- sample(which(d$Class == 1), sum(d$Class == 1) / ir , replace = FALSE)
  d <- d[c(idx.0,idx.1),, drop = FALSE]

  ## q-classifier
  oq <- imbalanced(Class ~ ., d, splitrule = "auc",
              importance = TRUE, block.size = 10)

  ## subsample the q-classifier
  smp.oq <- subsample(oq, B = 100)
  plot(smp.oq, cex.axis = .7)

}


# }

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