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I understand that by filtering out the instances with labels that Random Forest trees are uncertain upon with their decisions, and model these with another classifier could give a better overall result. My question is, how can I "combine" two (or more) classifiers' classification on a single unlabeled dataset?

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  • $\begingroup$ Well, weighted average or majority vote, but are you asking for more than that? Can you clarify what you are referring to in the first part? $\endgroup$ – Sean Owen Apr 10 '15 at 21:34
  • $\begingroup$ My question more precisely is: when I find out which labels are for whom my RF classifier uncertain is (by voting), I could train another (say, SVM) classifier exclusively for these uncertain labels. I do this by filtering out the RF-certain labels, and the remaining subset (with the unsure labels) is the training set for my SVM model. But how could I technically combine the RF and the SVM for an unseen new dataset with all the possible labels? In R one could classify ("predict") a given unlabeled dataset with only one model. $\endgroup$ – Fredrik Apr 11 '15 at 4:28
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Here's a solution using the caret package for R. A Random Forest is first trained on the data. All observations for which the probability (from the voting) is less than 99% are then passed to model 2, linear discriminant analysis. Only the probabilities from unseen resampling observations are used, since the Random Forest will otherwise fit the training data perfectly. That is what caret is needed for.

The accuracy is a little higher for the uncertain cases, but this is probably overfitting since I have tried several different models and the data set is small.

I'd like to know if this really improves the performance in your application for the out of sample test data. Are there any papers that recommend this approach? This approach seems to resemble boosting. I tried it on some of my data but could not improve the out of sample performance I got from model 1 (a Random Forest).

data(iris)
library(caret)
myTrainControl <- trainControl(method = "cv", number = 10,
                               savePredictions = T,
                               classProbs = TRUE)
set.seed(4213) # To get the same resamples every time
M1 <- train(y = iris$Species,
            x = iris[, !(names(iris) == "Species")],
            method = "rf",
            trControl = myTrainControl)

M1pred <- M1$pred[M1$pred$mtry == 2, ]
confusionMatrix(M1pred$pred, M1pred$obs)
# Accuracy 96%

# Inspect the predicted class probabilities:
probs <- cbind(M1pred$setosa,
                   M1pred$versicolor,
               M1pred$virginica)
colnames(probs) <- c("setosa", "versicolor", "virginica")
maxCol <- max.col(probs)
probs <- cbind(probs, maxCol)
maxProbs <- apply(probs, 1, function(x) x[x["maxCol"]])
summary(maxProbs)
# Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
# 0.5120  0.9805  0.9980  0.9645  1.0000  1.0000

# Let's define anything below 99% as uncertain:
uncertain <- which(maxProbs < 0.99)
length(uncertain) # 45
# Find rows in iris data that belong to 'uncertain' cases:
uncertainIndex <- M1pred$rowIndex[uncertain]
    confusionMatrix(M1pred$pred[uncertain],
                reference = M1pred$obs[uncertain])
# M1 Performance in uncertain cases:
#              Reference
# Prediction   setosa versicolor virginica
# setosa          5          0         0
# versicolor      0         17         3
# virginica       0          3        17
#
# Overall Statistics
# Accuracy : 0.8667

# Train new model on uncertain data only:
irisUncertain <- iris[uncertainIndex, ]
set.seed(4213) # To get the same resamples every time
M2 <- train(y = irisUncertain$Species,
            x = irisUncertain[, !(names(irisUncertain) == "Species")],
            method = "lda",
            trControl = myTrainControl)

M2pred <- M2$pred

confusionMatrix(M2pred$pred, reference = M2pred$obs)
#              Reference
# Prediction   setosa versicolor virginica
# setosa          4          0         0
# versicolor      1         16         0
# virginica       0          4        20
# 
# Overall Statistics
# Accuracy : 0.8889 
# (Small discrepancy: Why does caret report an accuracy of 88,5% for M2?)

# For new data predictions can be made as follows:
# (just as an example from the original data again)
# Some 'uncertain' cases are 'certain' now using the full M2 model
newdat <- irisUncertain[30:34, -5]
M1maxProbs <- apply(predict(M1, newdat, type = "prob"), 1, max)
ifelse(M1maxProbs < 0.99,
       paste("M2:", predict(M2, newdat)),
       paste("M1:", predict(M1, newdat)))
# 85               94              107              126 
# "M2: versicolor" "M1: versicolor"  "M2: virginica"  "M1: virginica" 
# 71 
# "M2: virginica"  
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