R: Compute out-of-bag cross-validated feature contributions to...

forestFloor {forestFloor} | R Documentation

## Compute out-of-bag cross-validated feature contributions to visualize model structures of randomForest models.

### Description

Computes a cross validated feature contribution matrix from a randomForest model-fit and outputs a forestFloor S3 class object (a list), including unscaled importance and the original training set. The output object is the basis for all visualizations.

### Usage

    forestFloor(rf.fit, X, Xtest=NULL, calc_np = FALSE, binary_reg = FALSE,
                bootstrapFC = FALSE, ...)

### Arguments

`rf.fit` | rf.fit, a random forest object as the output from randomForest::randomForest Train objects from caret::train is also experimentally supported, see how in the last use example
`X` | data.frame of input variables, numeric(continuous), discrete(treated as continuous) or factors(categorical). n_rows observations and n_columns features. X MUST be the exact same data.frame as used to train the random forest, see above item. If rows are re-ordered, the observations will not match the inbag-matrix resulting in distorted feature contributions.
`Xtest` | data.frame of input variables, numeric(continuous), discrete(treated as continuous) or factors(categorical). n_rows test_examples and n_columns features Xtest MUST have same number and order of columns(variables) as X. Number of rows and order can vary.
`calc_np` | TRUE/FALSE. Calculate Node Predictions(TRUE) or reuse information from rf.fit(FALSE)? Slightly faster when FALSE for regression. calc_np=TRUE will only take effect for rf.fit of class "randomForest" and type="regression". This option, is only for developmental purposes. Just set =FALSE always, as function will override this choice if not appropriate.
`binary_reg` | boolean, if TRUE binary classification can be changed to "percentage votes" of class 1, and thus be treated as regression.
`bootstrapFC` | boolean, if TRUE an extra column is added to FCmatrix or one extra matrix to FCarray accounting for the minor feature contributions attributed to random bootstraps or stratifications. Mainly useful to check FC row sums actually are equal to OOB-CV predictions, or to tweak randomForest into a "probability forest"-like model.
`...` | For classification it is possible to manually set majorityTerminal=FALSE. For the randomForest classification implementation majorityTerminal is by default set to TRUE, as each tree uses majority vote within terminal nodes. In other implemenations terminal nodes are not neccesarily reduced by majority voting before aggregetion on ensemble level. majorityTerminal, does not apply to random forest regressions. impType = 1 or 2 and impScale = T / F and impClass = "factor level name" can modify what type importance to export from randomForest object to forestFloor object. imp-arguments are passed to `importance`

### Details

forestFloor computes out-of-bag cross validated feature contributions for a "randomForest" class object. Other packages will be supported in future, mail me a request. forestFloor guides you to discover the structure of a randomForest model fit. Check examples of how latent interactions can be identified with colour gradients.

What is FC, feature cotributions?: First, a local increment is the change of node prediction from parent to daughter node split by a given feature. Feature Contributions are the sums over all local increments for each observation for each feature divided by the number of trees. Thus a feature contribution summarizes the average outcome for all those times a given observation was split by a given feature. forestFloor use the inbag observations to calculate local increments, but only sum local increments over out-of-bag observations divided with OOBtimes. OOBtimes is the number of times a given observation have been out-of-bag, which is around ntrees / 3. In practice this removes a substantial self-leverage of observations to the corresponding feature contributions. Hereby visualizations becomes less noisy.

What is FC used for?: Feature contributions is smart way to decompose a RF mapping structure into additive components. Plotting FC's against variables values yields at first glance plots similar to marginal-effect plots, partial dependence plots and vector effect characteristic plots. This package forestFloor, makes use of feature contributions to separate main effects and identify plus quantify interactions. The advantages of forestFloor over typical partial.dependence plots are: (1) Easier to identify interactions. (2) feature contributions do not extrapolate the training observations as partial.dependence will do for correlated features. (3) The "goodness of visualization" (how exactly the plot represent the higher dimensional model structure) can be quantified. (4) Cheerful colours and 3D graphics thanks to the rgl package.

RF regression takes input features and outputs a target value. RF classification can output a pseudo probability vector with predicted class probability for each prediction. The RF mapping dimensionality for classification is different than for regression, as the output is no longer a scalar. The output is a vector with predicted class probability for each class. For binary classification this mapping can be simplified to a regression-like scalar as the probability of class_1 = 1 - class_2. Set binary_reg=TRUE for a binary RF classification to get regression like visualizations. For multi-class the output space is a probability space where any point is a probability prediction of each target class.

To plot forestFloor objects use plot-method plot.forestFloor and function show3d. Input parameters for classification or regression are not entirely the same. Check help-file `plot.forestFloor` and `show3d`. For 3-class problems the special function `plot_simplex3` can plot the probability predictions in a 2D phase diagram (K-1 simplex).

### Value

the forestFloor function outputs(depending on type rf.fit) an object of either class "forestFloor_regression" or "forestFloor_multiClass" with following elements:

`X` | a copy of the training data or feature space matrix/data.frame, X. The copy is passed unchanged from the input of this function. X is used in all visualization to expand the feature contributions over the features of which they were recorded.
`Y` | a copy of the target vector, Y.
`importance` | The gini-importance or permutation-importance a.k.a variable importance of the random forest object (unscaled). If rfo=randomForest(X,Y,importance=FALSE), gini-importance is used. Gini-importance is less reproducible and more biased. The extra time used to compute permutation-importance is negligible.
`imp_ind` | the importance indices is the order to sort the features by descending importance. imp_ind is used by plotting functions to present most relevant feature contributions first. If using gini-importance, the order of plots is more random and will favor continuous variables. The plots themselves will not differ.
`FC_matrix` | [ONLY forestFloor_regression.] feature contributions in a matrix. n_row observations and n_column features - same dimensions as X.
`FC_array` | [ONLY forestFloor_multiClass.] feature contributions in a array. n_row observations and n_column features and n_layer classes. First two dimensions will match dimensions of X.

### Note

for more information goto forestFloor.dk

### Author(s)

Soren Havelund Welling

### References

Interpretation of QSAR Models Based on Random Forest Methods, http://dx.doi.org/10.1002/minf.201000173
Interpreting random forest classification models using a feature contribution method, http://arxiv.org/abs/1312.1121

### See Also

`plot.forestFloor`, `show3d`,

### Examples

    ## Not run:
    ## avoid testing of rgl 3D plot on headless non-windows OS
    ## users can disregard this sentence.
    if(!interactive() && Sys.info()["sysname"]!="Windows") skipRGL=TRUE

    #1 - Regression example:
    set.seed(1234)
    library(forestFloor)
    library(randomForest)

    #simulate data y = x1^2+sin(x2*pi)+x3*x4 + noise
    obs = 5000 #how many observations/samples
    vars = 6   #how many variables/features
    #create 6 normal distr. uncorr. variables
    X = data.frame(replicate(vars,rnorm(obs)))
    #create target by hidden function
    Y = with(X, X1^2 + sin(X2*pi) + 2 * X3 * X4 + 0.5 * rnorm(obs))

    #grow a forest
    rfo = randomForest(
      X, #features, data.frame or matrix. Recommended to name columns.
      Y, #targets, vector of integers or floats
      keep.inbag = TRUE,  # mandatory,
      importance = TRUE,  # recommended, else ordering by giniImpurity (unstable)
      sampsize = 1500 ,   # optional, reduce tree sizes to compute faster
      ntree = if(interactive()) 500 else 50 #speedup CRAN testing
    )

    #compute forestFloor object, often only 5-10% time of growing forest
    ff = forestFloor(
      rf.fit = rfo,       # mandatory
      X = X,              # mandatory
      calc_np = FALSE,    # TRUE or FALSE both works, makes no difference
      binary_reg = FALSE  # takes no effect here when rfo$type="regression"
    )

    #print forestFloor
    print(ff) #prints a text of what an 'forestFloor_regression' object is
    plot(ff)

    #plot partial functions of most important variables first
    plot(ff,                       # forestFloor object
         plot_seq = 1:6,           # optional sequence of features to plot
         orderByImportance=TRUE    # if TRUE index sequence by importance, else by X column
    )

    #Non interacting features are well displayed, whereas X3 and X4 are not
    #by applying color gradient, interactions reveal themself
    #also a k-nearest neighbor fit is applied to evaluate goodness-of-fit
    Col=fcol(ff,3,orderByImportance=FALSE) #create color gradient see help(fcol)
    plot(ff,col=Col,plot_GOF=TRUE)

    #feature contributions of X3 and X4 are well explained in the context of X3 and X4
    # as GOF R^2>.8

    show3d(ff,3:4,col=Col,plot_GOF=TRUE,orderByImportance=FALSE)

    #if needed, k-nearest neighbor parameters for goodness-of-fit can be accessed through convolute_ff
    #a new fit will be calculated and saved to forstFloor object as ff$FCfit
    ff = convolute_ff(ff,userArgs.kknn=alist(kernel="epanechnikov",kmax=5))
    plot(ff,col=Col,plot_GOF=TRUE) #this computed fit is now used in any 2D plotting.

    ###
    #2 - Multi classification example:   (multi is more than two classes)
    set.seed(1234)
    library(forestFloor)
    library(randomForest)

    data(iris)
    X = iris[,!names(iris) %in% "Species"]
    Y = iris[,"Species"]

    rf = randomForest(
      X,Y,
      keep.forest=TRUE,  # mandatory
      keep.inbag=TRUE,   # mandatory
      samp=20,           # reduce complexity of mapping structure, with same OOB%-explained
      importance  = TRUE # recommended, else ordering by giniImpurity (unstable)
    )

    ff = forestFloor(rf,X)

    plot(ff,plot_GOF=TRUE,cex=.7,
         colLists=list(c("#FF0000A5"),
                       c("#00FF0050"),
                       c("#0000FF35")))

    #...and 3D plot, see show3d
    show3d(ff,1:2,1:2,plot_GOF=TRUE)

    #...and simplex plot (only for three class problems)
    plot_simplex3(ff)
    plot_simplex3(ff,zoom.fit = TRUE)

    #...and 3d simplex plots (rough look, Z-axis is feature)
    plot_simplex3(ff,fig3d = TRUE)

    ###
    #3 - binary regression example
    #classification of two classes can be seen as regression in 0 to 1 scale
    set.seed(1234)
    library(forestFloor)
    library(randomForest)
    data(iris)
    X = iris[-1:-50,!names(iris) %in% "Species"] #drop third class virginica
    Y = iris[-1:-50,"Species"]
    Y = droplevels((Y)) #drop unused level virginica

    rf = randomForest(
      X,Y,
      keep.forest=TRUE,  # mandatory
      keep.inbag=TRUE,   # mandatory
      samp=20,           # reduce complexity of mapping structure, with same OOB%-explained
      importance  = TRUE # recommended, else giniImpurity
    )

    ff = forestFloor(rf,X,
                     calc_np=TRUE,    #mandatory to recalculate
                     binary_reg=TRUE) #binary regression, scale direction is printed
    Col = fcol(ff,1) #color by most important feature
    plot(ff,col=Col)   #plot features

    #interfacing with rgl::plot3d
    show3d(ff,1:2,col=Col,plot.rgl.args = list(size=2,type="s",alpha=.5))

    ##example with caret

    rm(list=ls())
    library(caret)
    library(forestFloor)
    N = 1000
    vars = 15
    noise_factor = .3
    bankruptcy_baserate = 0.2
    X = data.frame(replicate(vars,rnorm(N)))
    y.signal = with(X,X1^2+X2^2+X3*X4+X5+X6^3+sin(X7*pi)*2) #some non-linear f
    y.noise = rnorm(N) * sd(y.signal) * noise_factor
    y.total = y.noise+y.signal
    y = factor(y.total>=quantile(y.total,1-bankruptcy_baserate))

    set.seed(1)
    caret_train_obj <- train(
      x = X, y = y,
      method = "rf",
      keep.inbag = TRUE,  #always set keep.inbag=TRUE passed as ... parameter to randomForest
      ntree=50, #speed up this example, if set too low, forestFloor will fail
     )

    rf = caret_train_obj$finalModel #extract model
    if(!all(rf$y==y)) warning("seems like training set have been resampled, using smote?")
    ff = forestFloor(rf,X,binary_reg = T)

    #... or simply pass train
    ff = forestFloor(caret_train_obj,X,binary_reg = T)
    plot(ff,1:6,plot_GOF = TRUE)

    ## End(Not run)

[Package forestFloor version 1.11.1 Index]