Oblique random forest control

## Usage

```
orsf_control(
tree_type,
method,
scale_x,
ties,
net_mix,
target_df,
max_iter,
epsilon,
...
)
orsf_control_classification(
method = "glm",
scale_x = TRUE,
net_mix = 0.5,
target_df = NULL,
max_iter = 20,
epsilon = 1e-09,
...
)
orsf_control_regression(
method = "glm",
scale_x = TRUE,
net_mix = 0.5,
target_df = NULL,
max_iter = 20,
epsilon = 1e-09,
...
)
orsf_control_survival(
method = "glm",
scale_x = TRUE,
ties = "efron",
net_mix = 0.5,
target_df = NULL,
max_iter = 20,
epsilon = 1e-09,
...
)
```

## Arguments

- tree_type
(

*character*) the type of tree. Valid options are"classification", i.e., categorical outcomes

"regression", i.e., continuous outcomes

"survival", i.e., time-to event outcomes

- method
(

*character*or*function*) how to identify linear linear combinations of predictors. If`method`

is a character value, it must be one of:'glm': linear, logistic, and cox regression

'net': same as 'glm' but with penalty terms

'pca': principal component analysis

'random': random draw from uniform distribution

If

`method`

is a*function*, it will be used to identify linear combinations of predictor variables.`method`

must in this case accept three inputs named`x_node`

,`y_node`

and`w_node`

, and should expect the following types and dimensions:`x_node`

(*matrix*;`n`

rows,`p`

columns)`y_node`

(*matrix*;`n`

rows,`2`

columns)`w_node`

(*matrix*;`n`

rows,`1`

column)

In addition,

`method`

must return a matrix with p rows and 1 column.- scale_x
(

*logical*) if`TRUE`

, values of predictors will be scaled prior to each instance of finding a linear combination of predictors, using summary values from the data in the current node of the decision tree.- ties
(

*character*) a character string specifying the method for tie handling. Only relevant when modeling survival outcomes and using a method that engages with tied outcome times. If there are no ties, all the methods are equivalent. Valid options are 'breslow' and 'efron'. The Efron approximation is the default because it is more accurate when dealing with tied event times and has similar computational efficiency compared to the Breslow method.- net_mix
(

*double*) The elastic net mixing parameter. A value of 1 gives the lasso penalty, and a value of 0 gives the ridge penalty. If multiple values of alpha are given, then a penalized model is fit using each alpha value prior to splitting a node.- target_df
(

*integer*) Preferred number of variables used in each linear combination. For example, with`mtry`

of 5 and`target_df`

of 3, we sample 5 predictors and look for the best linear combination using 3 of them.- max_iter
(

*integer*) iteration continues until convergence (see`eps`

above) or the number of attempted iterations is equal to`iter_max`

.- epsilon
(

*double*) When using most modeling based method, iteration continues in the algorithm until the relative change in some kind of objective is less than`epsilon`

, or the absolute change is less than`sqrt(epsilon)`

.- ...
Further arguments passed to or from other methods (not currently used).

## Value

an object of class `'orsf_control'`

, which should be used as
an input for the `control`

argument of orsf. Components are:

`tree_type`

: type of trees to fit`lincomb_type`

: method for linear combinations`lincomb_eps`

: epsilon for convergence`lincomb_iter_max`

: max iterations`lincomb_scale`

: to scale or not.`lincomb_alpha`

: mixing parameter`lincomb_df_target`

: target degrees of freedom`lincomb_ties_method`

: method for ties in survival time`lincomb_R_function`

: R function for custom splits

## Details

Adjust `scale_x`

*at your own risk*. Setting `scale_x = FALSE`

will
reduce computation time but will also make the `orsf`

model dependent
on the scale of your data, which is why the default value is `TRUE`

.

## Examples

First we load some relevant packages

```
set.seed(329730)
suppressPackageStartupMessages({
library(aorsf)
library(survival)
library(ranger)
library(riskRegression)
})
```

### Accelerated linear combinations

The accelerated ORSF ensemble is the default because it has a nice balance of computational speed and prediction accuracy. It runs a single iteration of Newton Raphson scoring on the Cox partial likelihood function to find linear combinations of predictors.

```
fit_accel <- orsf(pbc_orsf,
control = orsf_control_survival(),
formula = Surv(time, status) ~ . - id,
tree_seeds = 329)
```

### Linear combinations with Cox regression

Setting inputs in `orsf_control_survival`

to scale the X matrix and
repeat iterations until convergence allows you to run Cox regression in
each non-terminal node of each survival tree, using the regression
coefficients to create linear combinations of predictors:

```
control_cph <- orsf_control_survival(method = 'glm',
scale_x = TRUE,
max_iter = 20)
fit_cph <- orsf(pbc_orsf,
control = control_cph,
formula = Surv(time, status) ~ . - id,
tree_seeds = 329)
```

### Linear combinations with penalized cox regression

Setting `method == 'net'`

runs penalized Cox regression in each
non-terminal node of each survival tree. This can be really helpful if
you want to do feature selection within the node, but it is a lot slower
than the `'glm'`

option.

```
# select 3 predictors out of 5 to be used in
# each linear combination of predictors.
control_net <- orsf_control_survival(method = 'net', target_df = 3)
fit_net <- orsf(pbc_orsf,
control = control_net,
formula = Surv(time, status) ~ . - id,
tree_seeds = 329)
```

### Linear combinations with your own function

In addition to the built-in methods, customized functions can be used to identify linear combinations of predictors. We’ll demonstrate a few here.

The first uses random coefficients

The second derives coefficients from principal component analysis

```
f_pca <- function(x_node, y_node, w_node) {
# estimate two principal components.
pca <- stats::prcomp(x_node, rank. = 2)
# use the second principal component to split the node
pca$rotation[, 1L, drop = FALSE]
}
```

The third uses

`ranger()`

inside of`orsf()`

. This approach is very similar to a method known as reinforcement learning trees (see the`RLT`

package), although our method of “muting” is very crude compared to the method proposed by Zhu et al.

```
f_rlt <- function(x_node, y_node, w_node){
colnames(y_node) <- c('time', 'status')
colnames(x_node) <- paste("x", seq(ncol(x_node)), sep = '')
data <- as.data.frame(cbind(y_node, x_node))
if(nrow(data) <= 10)
return(matrix(runif(ncol(x_node)), ncol = 1))
fit <- ranger::ranger(data = data,
formula = Surv(time, status) ~ .,
num.trees = 25,
num.threads = 1,
min.node.size = 5,
importance = 'permutation')
out <- sort(fit$variable.importance, decreasing = TRUE)
# "mute" the least two important variables
n_vars <- length(out)
if(n_vars > 4){
out[c(n_vars, n_vars-1)] <- 0
}
# ensure out has same variable order as input
out <- out[colnames(x_node)]
# protect yourself
out[is.na(out)] <- 0
matrix(out, ncol = 1)
}
```

We can plug these functions into `orsf_control_custom()`

, and then pass
the result into `orsf()`

:

```
fit_rando <- orsf(pbc_orsf,
Surv(time, status) ~ . - id,
control = orsf_control_survival(method = f_rando),
tree_seeds = 329)
fit_pca <- orsf(pbc_orsf,
Surv(time, status) ~ . - id,
control = orsf_control_survival(method = f_pca),
tree_seeds = 329)
fit_rlt <- orsf(pbc_orsf, time + status ~ . - id,
control = orsf_control_survival(method = f_rlt),
tree_seeds = 329)
```

So which fit seems to work best in this example? Let’s find out by evaluating the out-of-bag survival predictions.

```
risk_preds <- list(
accel = fit_accel$pred_oobag,
cph = fit_cph$pred_oobag,
net = fit_net$pred_oobag,
rando = fit_rando$pred_oobag,
pca = fit_pca$pred_oobag,
rlt = fit_rlt$pred_oobag
)
sc <- Score(object = risk_preds,
formula = Surv(time, status) ~ 1,
data = pbc_orsf,
summary = 'IPA',
times = fit_accel$pred_horizon)
```

The AUC values, from highest to lowest:

`sc$AUC$score[order(-AUC)]`

```
## model times AUC se lower upper
## <fctr> <num> <num> <num> <num> <num>
## 1: net 1788 0.9151649 0.02025057 0.8754745 0.9548553
## 2: rlt 1788 0.9119200 0.02090107 0.8709547 0.9528854
## 3: accel 1788 0.9095628 0.02143250 0.8675558 0.9515697
## 4: cph 1788 0.9095628 0.02143250 0.8675558 0.9515697
## 5: rando 1788 0.9062197 0.02148854 0.8641029 0.9483365
## 6: pca 1788 0.8999479 0.02226683 0.8563057 0.9435901
```

And the indices of prediction accuracy:

`sc$Brier$score[order(-IPA), .(model, times, IPA)]`

```
## model times IPA
## <fctr> <num> <num>
## 1: net 1788 0.4905777
## 2: accel 1788 0.4806649
## 3: cph 1788 0.4806649
## 4: rlt 1788 0.4675228
## 5: pca 1788 0.4383995
## 6: rando 1788 0.4302814
## 7: Null model 1788 0.0000000
```

From inspection,

`net`

,`accel`

, and`rlt`

have high discrimination and index of prediction accuracy.`rando`

and`pca`

do less well, but they aren’t bad.

## See also

linear combination control functions
`orsf_control_cph()`

,
`orsf_control_custom()`

,
`orsf_control_fast()`

,
`orsf_control_net()`