outForest

outForest is a random forest regression based multivariate anomaly detection method. Each numeric variable is regressed onto all other variables using a random forest. If the scaled absolute difference between observed value and out-of-bag prediction is larger than a prespecified threshold, then a value is considered an outlier. After identification of outliers, they can be replaced e.g. by predictive mean matching from the non-outliers.

The method can be viewed as a multivariate extension of a basic univariate outlier detection method where a value is considered an outlier if it is more than e.g. three times the standard deviation away from its mean. In the multivariate case, instead of comparing a value with the overall mean, rather the difference to the conditional mean is considered. The outForest package estimates this conditional mean by a random forest.

Once the method is trained on a reference data, it can be applied to new data.

Installation

From CRAN:

install.packages("outForest")

Latest version from github:

library(devtools)
install_github("mayer79/outForest", subdir = "release/outforest")

Examples

We first generate a data set with about 2% outliers values in each numeric column. Then, we try to identify them.

library(outForest)
set.seed(3)

# Generate data with outliers in numeric columns
head(irisWithOutliers <- generateOutliers(iris, p = 0.02))

# Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#          5.1    3.500000          1.4         0.2  setosa
#          4.9    3.000000          1.4         0.2  setosa
#          4.7    3.200000          1.3         0.2  setosa
#          4.6    3.100000          1.5         0.2  setosa
#          5.0   -3.744405          1.4         0.2  setosa
#          5.4    3.900000          1.7         0.4  setosa
 
# Find outliers by random forest regressions and replace them by predictive mean matching
(out <- outForest(irisWithOutliers, allow_predictions = TRUE))

# Plot the number of outliers per numeric variable
plot(out)

# Information on outliers
head(outliers(out))

# row          col  observed predicted      rmse     score threshold replacement
#   5  Sepal.Width -3.744405  3.298493 0.7810172 -9.017596         3         2.8
#  20 Sepal.Length 10.164017  5.141093 0.6750468  7.440852         3         5.4
# 138  Petal.Width  4.721186  2.113464 0.3712539  7.024092         3         2.1
#  68  Petal.Width -1.188913  1.305339 0.3712539 -6.718452         3         1.2
# 137  Sepal.Width  8.054524  2.861445 0.7810172  6.649122         3         2.9
#  15 Petal.Length  6.885277  1.875646 0.7767877  6.449163         3         1.3

# Resulting data set with replaced outliers
head(Data(out))

# Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#          5.1         3.5          1.4         0.2  setosa
#          4.9         3.0          1.4         0.2  setosa
#          4.7         3.2          1.3         0.2  setosa
#          4.6         3.1          1.5         0.2  setosa
#          5.0         2.8          1.4         0.2  setosa
#          5.4         3.9          1.7         0.4  setosa

# Out-of-sample application
iris1 <- iris[1, ]
iris1$Sepal.Length <- -1
pred <- predict(out, newdata = iris1)

# Did we find the outlier?
outliers(pred)

# row          col observed predicted      rmse    score threshold replacement
#   1 Sepal.Length       -1  4.960069 0.6750468 -8.82912         3         6.4

# Fixed data
Data(pred)

# Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#          6.4         3.5          1.4         0.2  setosa