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This article covers core features of the aorsf package.

Background

The oblique random forest (RF) is an extension of the traditional (axis-based) RF. Instead of using a single variable to split data and grow new branches, trees in the oblique RF use a weighted combination of multiple variables.

Oblique RFs for survival, classification, and regression

The purpose of aorsf (‘a’ is short for accelerated) is to provide a unifying framework to fit oblique RFs that can scale adequately to large data sets. The fastest algorithms available in the package are used by default because they often have equivalent prediction accuracy to more computational approaches.

The center piece of aorsf is the orsf() function. In the initial versions of aorsf, the orsf() function only fit oblique random survival forests, but now it allows for classification, regression, and survival forests. (I may introduce an orf() function in the future if the name orsf() is misleading to users.)

For classification, we fit an oblique RF to predict penguin species using penguin data from the magnificent palmerpenguins R package

# An oblique classification RF
penguin_fit <- orsf(data = penguins_orsf, formula = species ~ .)

penguin_fit
#> ---------- Oblique random classification forest
#> 
#>      Linear combinations: Accelerated Logistic regression
#>           N observations: 333
#>                N classes: 3
#>                  N trees: 500
#>       N predictors total: 7
#>    N predictors per node: 3
#>  Average leaves per tree: 5.61
#> Min observations in leaf: 5
#>           OOB stat value: 1.00
#>            OOB stat type: AUC-ROC
#>      Variable importance: anova
#> 
#> -----------------------------------------

For regression, we use the same data but predict bill length of penguins:

# An oblique regression RF
bill_fit <- orsf(data = penguins_orsf, formula = bill_length_mm ~ .)

bill_fit
#> ---------- Oblique random regression forest
#> 
#>      Linear combinations: Accelerated Linear regression
#>           N observations: 333
#>                  N trees: 500
#>       N predictors total: 7
#>    N predictors per node: 3
#>  Average leaves per tree: 49.954
#> Min observations in leaf: 5
#>           OOB stat value: 0.82
#>            OOB stat type: RSQ
#>      Variable importance: anova
#> 
#> -----------------------------------------

My personal favorite is the oblique survival RF with accelerated Cox regression because it has a great combination of prediction accuracy and computational efficiency (see JCGS paper). Here, we predict mortality risk following diagnosis of primary biliary cirrhosis:

# An oblique survival RF
pbc_fit <- orsf(data = pbc_orsf, 
                n_tree = 5,
                formula = Surv(time, status) ~ . - id)

pbc_fit
#> ---------- Oblique random survival forest
#> 
#>      Linear combinations: Accelerated Cox regression
#>           N observations: 276
#>                 N events: 111
#>                  N trees: 5
#>       N predictors total: 17
#>    N predictors per node: 5
#>  Average leaves per tree: 21.4
#> Min observations in leaf: 5
#>       Min events in leaf: 1
#>           OOB stat value: 0.72
#>            OOB stat type: Harrell's C-index
#>      Variable importance: anova
#> 
#> -----------------------------------------

you may notice that the first input of aorsf is data. This is a design choice that makes it easier to use orsf with pipes (i.e., %>% or |>). For instance,


library(dplyr)

pbc_fit <- pbc_orsf |> 
 select(-id) |> 
 orsf(formula = Surv(time, status) ~ .,
      n_tree = 5)

Interpretation

aorsf includes several functions dedicated to interpretation of ORSFs, both through estimation of partial dependence and variable importance.

Variable importance

There are multiple methods to compute variable importance, and each can be applied to any type of oblique forest.

  • To compute negation importance, ORSF multiplies each coefficient of that variable by -1 and then re-computes the out-of-sample (sometimes referred to as out-of-bag) accuracy of the ORSF model.

    
    orsf_vi_negate(pbc_fit)
    #>          bili        copper       protime           age           sex 
    #>  0.0440377960  0.0420048466  0.0369341571  0.0252448224  0.0248793746 
    #>      alk.phos       ascites          chol       spiders           trt 
    #>  0.0190849320  0.0170516503  0.0148130677  0.0141720105  0.0104615534 
    #>         edema      platelet           ast          trig         stage 
    #>  0.0075941183  0.0057634675 -0.0009858459 -0.0029741607 -0.0069088510 
    #>       albumin        hepato 
    #> -0.0100788728 -0.0106202184
  • You can also compute variable importance using permutation, a more classical approach that noises up a predictor and then assigned the resulting degradation in prediction accuracy to be the importance of that predictor.

    
    orsf_vi_permute(penguin_fit)
    #>    bill_length_mm flipper_length_mm     bill_depth_mm            island 
    #>        0.17309067        0.10602941        0.07935065        0.06224106 
    #>       body_mass_g               sex              year 
    #>        0.05947613        0.01811280        0.00156581
  • A faster alternative to permutation and negation importance is ANOVA importance, which computes the proportion of times each variable obtains a low p-value (p < 0.01) while the forest is grown.

    
    orsf_vi_anova(bill_fit)
    #>           species               sex            island flipper_length_mm 
    #>        0.36494315        0.21489404        0.10946714        0.08796023 
    #>       body_mass_g     bill_depth_mm              year 
    #>        0.07479824        0.06392848        0.01312852

Partial dependence (PD)

Partial dependence (PD) shows the expected prediction from a model as a function of a single predictor or multiple predictors. The expectation is marginalized over the values of all other predictors, giving something like a multivariable adjusted estimate of the model’s prediction.

For more on PD, see the vignette

Individual conditional expectations (ICE)

Unlike partial dependence, which shows the expected prediction as a function of one or multiple predictors, individual conditional expectations (ICE) show the prediction for an individual observation as a function of a predictor.

For more on ICE, see the vignette

What about the original ORSF?

The original ORSF (i.e., obliqueRSF) used glmnet to find linear combinations of inputs. aorsf allows users to implement this approach using the orsf_control_survival(method = 'net') function:


orsf_net <- orsf(data = pbc_orsf, 
                 formula = Surv(time, status) ~ . - id, 
                 control = orsf_control_survival(method = 'net'))

net forests fit a lot faster than the original ORSF function in obliqueRSF. However, net forests are still much slower than cph ones.

aorsf and other machine learning software

The unique feature of aorsf is its fast algorithms to fit ORSF ensembles. RLT and obliqueRSF both fit oblique random survival forests, but aorsf does so faster. ranger and randomForestSRC fit survival forests, but neither package supports oblique splitting. obliqueRF fits oblique random forests for classification and regression, but not survival. PPforest fits oblique random forests for classification but not survival.

Note: The default prediction behavior for aorsf models is to produce predicted risk at a specific prediction horizon, which is not the default for ranger or randomForestSRC. I think this will change in the future, as computing time independent predictions with aorsf could be helpful.

Learning more

aorsf began as a dedicated package for oblique random survival forests, and so most papers published so far have focused on survival analysis and risk prediction. However, the routines for regression and classification oblique RFs in aorsf have high overlap with the survival ones.

  • See orsf for more details on oblique random survival forests.

  • see the JCGS paper for more details on algorithms used specifically by aorsf.