BT {BT} | R Documentation |

## (Adaptive) Boosting Trees (ABT/BT) Algorithm.

### Description

Performs the (Adaptive) Boosting Trees algorithm. This code prepares the inputs and calls the function `BT_call`

.
Each tree in the process is built thanks to the `rpart`

function.
In case of cross-validation, this function prepares the folds and performs multiple calls to the fitting function `BT_call`

.

### Usage

```
BT(
formula = formula(data),
data = list(),
tweedie.power = 1,
ABT = TRUE,
n.iter = 100,
train.fraction = 1,
interaction.depth = 4,
shrinkage = 1,
bag.fraction = 1,
colsample.bytree = NULL,
keep.data = TRUE,
is.verbose = FALSE,
cv.folds = 1,
folds.id = NULL,
n.cores = 1,
tree.control = rpart.control(xval = 0, maxdepth = (if (!is.null(interaction.depth)) {
interaction.depth
} else {
10
}), cp = -Inf, minsplit = 2),
weights = NULL,
seed = NULL,
...
)
```

### Arguments

`formula` |
a symbolic description of the model to be fit. Note that the offset isn't supported in this algorithm. Instead, everything is performed with a log-link function and a direct relationship exist between response, offset and weights. |

`data` |
an optional data frame containing the variables in the model. By default the variables are taken from |

`tweedie.power` |
Experimental parameter currently not used - Set to 1 referring to Poisson distribution. |

`ABT` |
a boolean parameter. If |

`n.iter` |
the total number of iterations to fit. This is equivalent to the number of trees and the number of basis functions in the additive expansion.
Please note that the initialization is not taken into account in the |

`train.fraction` |
the first |

`interaction.depth` |
the maximum depth of variable interactions: 1 builds an additive model, 2 builds a model with up to two-way interactions, etc.
This parameter can also be interpreted as the maximum number of non-terminal nodes. By default, it is set to 4.
Please note that if this parameter is |

`shrinkage` |
a shrinkage parameter (in the interval (0,1]) applied to each tree in the expansion. Also known as the learning rate or step-size reduction. By default, it is set to 1. |

`bag.fraction` |
the fraction of independent training observations randomly selected to propose the next tree in the expansion.
This introduces randomness into the model fit. If |

`colsample.bytree` |
each tree will be trained on a random subset of |

`keep.data` |
a boolean variable indicating whether to keep the data frames. This is particularly useful if one wants to keep track of the initial data frames
and is further used for predicting in case any data frame is specified.
Note that in case of cross-validation, if |

`is.verbose` |
if |

`cv.folds` |
a positive integer representing the number of cross-validation folds to perform. If |

`folds.id` |
an optional vector of values identifying what fold each observation is in. If supplied, this parameter prevails over |

`n.cores` |
the number of cores to use for parallelization. This parameter is used during the cross-validation. This parameter is bounded between 1 and the maximum number of available cores. By default, it is set to 1 leading to a sequential approach. |

`tree.control` |
for advanced user only. It allows to define additional tree parameters that will be used at each iteration.
See |

`weights` |
optional vector of weights used in the fitting process. These weights must be positive but do not need to be normalized.
By default, it is set to |

`seed` |
optional number used as seed. Please note that if |

`...` |
not currently used. |

### Details

The NA values are currently dropped using `na.omit`

.

### Value

a `BTFit`

object.

### Author(s)

Gireg Willame gireg.willame@gmail.com

*This package is inspired by the gbm3 package. For more details, see https://github.com/gbm-developers/gbm3/*.

### References

M. Denuit, D. Hainaut and J. Trufin (2019). **Effective Statistical Learning Methods for Actuaries |: GLMs and Extensions**, *Springer Actuarial*.

M. Denuit, D. Hainaut and J. Trufin (2019). **Effective Statistical Learning Methods for Actuaries ||: Tree-Based Methods and Extensions**, *Springer Actuarial*.

M. Denuit, D. Hainaut and J. Trufin (2019). **Effective Statistical Learning Methods for Actuaries |||: Neural Networks and Extensions**, *Springer Actuarial*.

M. Denuit, D. Hainaut and J. Trufin (2022). **Response versus gradient boosting trees, GLMs and neural networks under Tweedie loss and log-link**.
Accepted for publication in *Scandinavian Actuarial Journal*.

M. Denuit, J. Huyghe and J. Trufin (2022). **Boosting cost-complexity pruned trees on Tweedie responses: The ABT machine for insurance ratemaking**.
Paper submitted for publication.

M. Denuit, J. Trufin and T. Verdebout (2022). **Boosting on the responses with Tweedie loss functions**. Paper submitted for publication.

### See Also

`BTFit`

, `BTCVFit`

, `BT_call`

, `BT_perf`

, `predict.BTFit`

,
`summary.BTFit`

, `print.BTFit`

, `.BT_cv_errors`

.

### Examples

```
## Load dataset.
dataset <- BT::BT_Simulated_Data
## Fit a Boosting Tree model.
BT_algo <- BT(formula = Y_normalized ~ Age + Sport + Split + Gender, # formula
data = dataset, # data
ABT = FALSE, # Classical Boosting Tree
n.iter = 200,
train.fraction = 0.8,
interaction.depth = 3,
shrinkage = 0.01,
bag.fraction = 0.5,
colsample.bytree = 2, # 2 explanatory variable used at each iteration.
keep.data = FALSE, # Do not keep a data copy.
is.verbose = FALSE, # Do not print progress.
cv.folds = 3, # 3-cv will be performed.
folds.id = NULL ,
n.cores = 1,
weights = ExpoR, # <=> Poisson model on response Y with ExpoR in offset.
seed = NULL)
## Determine the model performance and plot results.
best_iter_val <- BT_perf(BT_algo, method='validation')
best_iter_oob <- BT_perf(BT_algo, method='OOB', oobag.curve = TRUE)
best_iter_cv <- BT_perf(BT_algo, method ='cv', oobag.curve = TRUE)
best_iter <- best_iter_val
## Variable influence and plot results.
# Based on the first iteration.
variable_influence1 <- summary(BT_algo, n.iter = 1)
# Using all iterations up to best_iter.
variable_influence_best_iter <- summary(BT_algo, n.iter = best_iter)
## Print results : call, best_iters and summarized relative influence.
print(BT_algo)
## Model predictions.
# Predict on the link scale, using only the best_iter tree.
pred_single_iter <- predict(BT_algo, newdata = dataset,
n.iter = best_iter, type = 'link', single.iter = TRUE)
# Predict on the response scale, using the first best_iter.
pred_best_iter <- predict(BT_algo, newdata = dataset,
n.iter = best_iter, type = 'response')
```

*BT*version 0.4 Index]