R: Hold out variable importance (VIMP)

holdout.vimp.rfsrc {randomForestSRC} | R Documentation

## Hold out variable importance (VIMP)

### Description

Hold out VIMP is calculated from the error rate of mini ensembles of trees (blocks of trees) grown with and without a variable. Applies to all families.

### Usage

    ## S3 method for class 'rfsrc'
    holdout.vimp(formula, data,
      ntree = function(p, vtry){1000 * p / vtry},
      nsplit = 10,
      ntime = 50,
      sampsize = function(x){x * .632},
      samptype = "swor",
      block.size = 10,
      vtry = 1,
      ...)

### Arguments

`formula` | A symbolic description of the model to be fit.
`data` | Data frame containing the y-outcome and x-variables.
`ntree` | Function specifying requested number of trees used for growing the forest. Inputs are dimension and number of holdout variables. The requested number of trees can also be a number.
`nsplit` | Non-negative integer value specifying number of random split points used to split a node (deterministic splitting corresponds to the value zero and is much slower).
`ntime` | Integer value used for survival to constrain ensemble calculations to a grid of `ntime` time points.
`sampsize` | Function specifying size of subsampled data. Can also be a number.
`samptype` | Type of bootstrap used.
`vtry` | Number of variables randomly selected to be held out when growing a tree. This can also be set to a list for a targeted hold out VIMP analysis. See details below for more information.
`block.size` | Specifies number of trees in a block when calculating holdout variable importance.
`...` | Further arguments to be passed to `rfsrc`.

### Details

Holdout variable importance (holdout VIMP) is based on comparing the results of two mini forests of trees (blocks of trees), the first in which a random set of `vtry` features are held out (the holdout forest), and the second in which no features are held out (the baseline forest). The mini forests are constructed from blocks of trees, where if the block size is one, then this is similar to the idea of Breiman-Cutler which calculates permuation VIMP using one tree at a time.

If a feature is held out in a block of trees, we refer to this as the (feature, block) pair. The bootstrap for the trees in a (feature, block) pair are identical in both forests. That is, the holdout block is grow by holding out the feature, and the baseline block is grown over the same trees, with the same bootstrap, but without holding out any features. `vtry` controls how many features are held out in every tree. If set to one (default), only one variable is held out in every tree. Once a (feature, block) of trees has been grown, holdout VIMP for a given variable v is calculated as follows. Gather the block of trees where the feature was held out (from the holdout forest) and calculate OOB prediction error. Next gather the corresponding block of trees where v was not held out (from the baseline forest) and calculate OOB prediction error. Holdout VIMP for the (feature, block) pair is the difference between these two values. The final holdout VIMP estimate for a feature v is obtained by averaging holdout VIMP for (feature=v, block) over all blocks.

To summarize, holdout VIMP measures the importance of a variable when that variable is truly removed from growing the tree.

Accuracy of hold out VIMP depends critically on total number of trees. If total number of trees is too small, then number of times a variable is held out will be small and OOB error can suffer from high variance. Therefore, `ntree` should be set fairly high - we recommend using 1000 times the number of features. Increasing `vtry` is another way to increase number of times a variable is held out and therefore reduces the burden of growing a large number of trees. In particular, total number of trees needed decreases linearly with `vtry`. The default `ntree` equals 1000 trees for each feature divided by `vtry`. Keep in mind intrepretation of holdout VIMP is altered when `vtry` is different than one. Thus this option should be used with caution.

Accuracy also depends on the value of `blocksize`. Smaller values generally produce better results but are more computationally demanding. The value of `blocksize` should not exceed `ntree` divided by number of features, otherwise there may not be enough trees to satisify the target block size for a feature and missing values will result.

Finally, we note that a targeted hold out VIMP analysis can be requested by setting `vtry` to a list with two entries. The first entry is a vector of integer values specifying the variables of interest. The second entry is a boolean logical flag indicating whether individual or joint VIMP should be calculated. For example, suppose variables 1, 4 and 5 are our variables of interest. To calculate holdout VIMP for these variables, and these variables only, `vtry` would be specified by

vtry = list(xvar = c(1, 4, 5), joint = FALSE)

On the other hand, if we are interested in the joint effect when we remove the three variables simultaneously, then

vtry = list(xvar = c(1, 4, 5), joint = TRUE)

The benefits of a targeted analysis is that the user may have a pre-conceived idea of which variables are interesting. Only VIMP for these variables will be calculated which greatly reduces computational time. Another benefit is that when joint VIMP is requested, this provides the user with a way to assess importance of specific groups of variables. See the iris example below for illustration.

### Value

Invisibly a list with the following components (which themselves can be lists):

`importance` | Holdout VIMP.
`baseline` | Prediction error for the baseline forest.
`holdout` | Prediction error for the holdout forest.

### Author(s)

Hemant Ishwaran and Udaya B. Kogalur

### References

Lu M. and Ishwaran H. (2018). Expert Opinion: A prediction-based alternative to p-values in regression models. J. Thoracic and Cardiovascular Surgery, 155(3), 1130–1136.

### See Also

`vimp.rfsrc`

### Examples

    ## ------------------------------------------------------------
    ## regression analysis
    ## ------------------------------------------------------------

    ## new York air quality measurements
    airq.obj <- holdout.vimp(Ozone ~ ., data = airquality, na.action = "na.impute")
    print(airq.obj$importance)

    ## ------------------------------------------------------------
    ## classification analysis
    ## ------------------------------------------------------------

    ## iris data
    iris.obj <- holdout.vimp(Species ~., data = iris)
    print(iris.obj$importance)

    ## iris data using brier prediction error
    iris.obj <- holdout.vimp(Species ~., data = iris, perf.type = "brier")
    print(iris.obj$importance)

    ## ------------------------------------------------------------
    ## illustration of targeted holdout vimp analysis
    ## ------------------------------------------------------------

    ## iris data - only interested in variables 3 and 4
    vtry <- list(xvar = c(3, 4), joint = FALSE)
    print(holdout.vimp(Species ~., data = iris, vtry = vtry)$impor)

    ## iris data - joint importance of variables 3 and 4
    vtry <- list(xvar = c(3, 4), joint = TRUE)
    print(holdout.vimp(Species ~., data = iris, vtry = vtry)$impor)

    ## iris data - joint importance of variables 1 and 2
    vtry <- list(xvar = c(1, 2), joint = TRUE)
    print(holdout.vimp(Species ~., data = iris, vtry = vtry)$impor)

    ## ------------------------------------------------------------
    ## imbalanced classification (using RFQ)
    ## ------------------------------------------------------------

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

      ## experimental settings
      n <- 400
      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 RFQ with and without blocking
      vmp1 <- imbalanced(f, d, importance = TRUE, block.size = 1)$importance[, 1]
      vmp10 <- imbalanced(f, d, importance = TRUE, block.size = 10)$importance[, 1]

      ## holdout VIMP for RFQ with and without blocking
      hvmp1 <- holdout.vimp(f, d, rfq =  TRUE,
                   perf.type = "g.mean", block.size = 1)$importance[, 1]
      hvmp10 <- holdout.vimp(f, d, rfq =  TRUE,
                   perf.type = "g.mean", block.size = 10)$importance[, 1]

      ## compare VIMP values
      imp <- 100 * cbind(vmp1, vmp10, hvmp1, hvmp10)
      legn <- c("vimp-1", "vimp-10","hvimp-1", "hvimp-10")
      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)

    }

    ## ------------------------------------------------------------
    ## multivariate regression analysis
    ## ------------------------------------------------------------
    mtcars.mreg <- holdout.vimp(Multivar(mpg, cyl) ~., data = mtcars,
                                        vtry = 3,
                                        block.size = 1,
                                        samptype = "swr",
                                        sampsize = dim(mtcars)[1])
    print(mtcars.mreg$importance)

    ## ------------------------------------------------------------
    ## mixed outcomes analysis
    ## ------------------------------------------------------------

    mtcars.new <- mtcars
    mtcars.new$cyl <- factor(mtcars.new$cyl)
    mtcars.new$carb <- factor(mtcars.new$carb, ordered = TRUE)
    mtcars.mix <- holdout.vimp(cbind(carb, mpg, cyl) ~., data = mtcars.new,
                                       ntree = 100,
                                       block.size = 2,
                                       vtry = 1)
    print(mtcars.mix$importance)

    ##------------------------------------------------------------
    ## survival analysis
    ##------------------------------------------------------------

    ## Primary biliary cirrhosis (PBC) of the liver
    data(pbc, package = "randomForestSRC")
    pbc.obj <- holdout.vimp(Surv(days, status) ~ ., pbc,
                                    nsplit = 10,
                                    ntree = 1000,
                                    na.action = "na.impute")
    print(pbc.obj$importance)

    ##------------------------------------------------------------
    ## competing risks
    ##------------------------------------------------------------

    ## WIHS analysis
    ## cumulative incidence function (CIF) for HAART and AIDS stratified by IDU

    data(wihs, package = "randomForestSRC")
    wihs.obj <- holdout.vimp(Surv(time, status) ~ ., wihs,
                                     nsplit = 3,
                                     ntree = 100)
    print(wihs.obj$importance)

[Package randomForestSRC version 2.11.0 Index]