Imbalanced Two Class Problems

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.

imbalanced(formula, data, ntree = 3000, 
  method = c("rfq", "brf", "standard"), splitrule = "auc",
  perf.type = NULL, block.size = NULL, fast = FALSE,
  ratio = NULL, ...)

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.

splitrule

Default is AUC splitting which maximizes gmean performance. Other choices are "gini" and "entropy".

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 gmean 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. If not specified, uses the default value specified in rfsrc.

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.

...

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

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.

Permutation VIMP is used by default and not anti-VIMP which is the default for all other families and settings. Our experiments indicate the former performs better in imbalanced settings, especially when imbalanced ratio is high.

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.

A new helper function get.imbalanced.performance has been added for extracting performance metrics. Metrics are self-titled and their meaning should generally be clear. Metrics that may be less familiar include: F1, the F-score or the F-measure which measures balance between the precision and the recall. F1mod, the harmonic mean of sensitivity, specificity, precision and the negative predictive value. F1gmean, the average of F1 and the G-mean. F1modgmean, the average of F1mod and the G-mean.

Value

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

Author

Hemant Ishwaran and Udaya B. Kogalur

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

See also

rfsrc, rfsrc.fast

Examples

# \donttest{
## ------------------------------------------------------------
## 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 = "gmean", splitrule = "auc") 

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

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

##-----------------------------------------------------------------
## RF using misclassification error with gini splitting
## ------------------------------------------------------------

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

##-----------------------------------------------------------------
## RF using G-mean performance with AUC splitting
## ------------------------------------------------------------

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

## equivalent to:
## rfsrc(f, breast, ntree = 3000, perf.type = "gmean", splitrule = "auc")

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

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

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

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

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

##----------------------------------------------------------------
## 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]))


##----------------------------------------------------------------
##
##  illustrates how to optimize threshold on training data
##  improves Gmean for RFQ in many situations
##
##----------------------------------------------------------------

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

  ## experimental settings
  n <- 2 * 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]

  ## split data into train and test
  trn.pt <- sample(1:nrow(d), size = nrow(d) / 2)
  trn <- d[trn.pt, ]
  tst <- d[setdiff(1:nrow(d), trn.pt), ]

  ## run rfq on training data
  o <- imbalanced(f, trn)

  ## (1) default threshold (2) directly optimized gmean threshold
  th.1 <- get.imbalanced.performance(o)["threshold"]
  th.2 <- get.imbalanced.optimize(o)["threshold"]

  ## training performance
  cat("-------- train performance ---------\n")
  print(get.imbalanced.performance(o, thresh=th.1))
  print(get.imbalanced.performance(o, thresh=th.2))

  ## test performance
  cat("-------- test performance ---------\n")
  pred.o <- predict(o, tst)
  print(get.imbalanced.performance(pred.o, thresh=th.1))
  print(get.imbalanced.performance(pred.o, thresh=th.2))
 
} 

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

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, ]))
  
}

##----------------------------------------------------------------
##
## 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]

  ## permutation 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 = "permute", block.size = 1)
  brfB <- imbalanced(f, d, method = "brf", importance = "permute", block.size = 10)

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

  ## RFQ
  o <- imbalanced(Class ~ ., d, importance = "permute", block.size = 10)

  ## subsample RFQ
  smp.o <- subsample(o, B = 100)
  plot(smp.o, cex.axis = .7)

}


# }