# Fitting Stochastic Boosting Models

### Description

‘ada’ is used to fit a variety stochastic boosting models for a binary response
as described in *Additive Logistic Regression: A Statistical
View of Boosting* by Friedman, et al. (2000).

### Usage

1 2 3 4 5 6 7 8 9 | ```
ada(x,...)
## Default S3 method:
ada(x, y,test.x,test.y=NULL, loss=c("exponential","logistic"),
type=c("discrete","real","gentle"),iter=50, nu=0.1, bag.frac=0.5,
model.coef=TRUE,bag.shift=FALSE,max.iter=20,delta=10^(-10),
verbose=FALSE,...,na.action=na.rpart)
## S3 method for class 'formula'
ada(formula, data, ..., subset, na.action=na.rpart)
``` |

### Arguments

`x` |
matrix of descriptors. |

`y` |
vector of responses. ‘y’ may have only two unique values. |

`test.x` |
testing matrix of discriptors (optional) |

`test.y` |
vector of testing responses (optional) |

`loss` |
loss="exponential", "ada","e" or any variation corresponds to the default boosting under exponential loss. loss="logistic","l2","l" provides boosting under logistic loss. |

`type` |
type of boosting algorithm to perform. “discrete” performs discrete Boosting (default). “real” performs Real Boost. “gentle” performs Gentle Boost. |

`iter` |
number of boosting iterations to perform. Default = 50. |

`nu` |
shrinkage parameter for boosting, default taken as 1. |

`bag.frac` |
sampling fraction for samples taken out-of-bag. This allows one to use random permutation which improves performance. |

`model.coef` |
flag to use stageweights in boosting. If FALSE then the procedure corresponds to epsilon-boosting. |

`bag.shift` |
flag to determine whether the stageweights should go to one as nu goes to zero. This only makes since if bag.frac is small. The rationale behind this parameter is discussed in (Culp et al., 2006). |

`max.iter` |
number of iterations to perform in the newton step to determine the coeficient. |

`delta` |
tolarence for convergence of the newton step to determine the coeficient. |

`verbose` |
print the number of iterations necessary for convergence of a coeficient. |

`formula` |
a symbolic description of the model to be fit. |

`data` |
an optional data frame containing the variables in the model. |

`subset` |
an optional vector specifying a subset of observations to be used in the fitting process. |

`na.action` |
a function that indicates how to process ‘NA’ values. Default=na.rpart. |

`...` |
arguments passed to |

### Details

This function directly follows the algorithms listed in *“Additive Logistic
Regression: A Statistical View of Boosting”*.

When using usage ‘ada(x,y)’: x data can take the form data.frame or as.matrix. y data can take form data.frame, as.factor, as.matrix, as.array, or as.table. Missing values must be removed from the data prior to execution.

When using usage ‘ada(y~.)’: data must be in a data frame. Response can have factor or numeric values. Missing values can be present in the descriptor data, whenever na.action is set to any option other than na.pass.

After the model is fit, ‘ada’ prints a summary of the function call, the method used for boosting, the number of iterations, the final confusion matrix (observed classification vs predicted classification; labels for classes are same as in response), the error for the training set, and testing, training , and kappa estimates of the appropriate number of iterations.

A summary of this information can also be obtained with the command ‘print(x)’.

Corresponding functions (Use help with summary.ada, predict.ada, ... varplot for additional information on these commands):

summary : function to print a summary of the original function call, method used for boosting, number of iterations, final confusion matrix, accuracy, and kappa statistic (a measure of agreement between the observed classification and predicted classification). ‘summary’ can be used for training, testing, or validation data.

predict : function to predict the response for any data set (train, test, or validation).

plot : function to plot performance of the algorithm across boosting iterations. Default plot is iteration number (x-axis) versus prediction error (y-axis) for the data set used to build the model. Function can also simultaneously produce an error plot for an external test set and a kappa plot for training and test sets.

pairs : function to produce pairwise plots of descriptors. Descriptors are arranged by decreasing frequency of selection by boosting (upper left = most frequently chosen). The color of the marker in the plot represents class membership; the Size of the marker represents predicted class probability. The larger the marker, the higher the probability of classification.

varplot : plot of variables ordered by the variable importance measure (based on improvement).

addtest : add a testing data set to the `ada`

object, therefore the testing errors only have to
be computed once.

update : add more trees to the `ada`

object.

### Value

`model` |
The following items are the different components created by the algorithms: trees: ensamble of rpart trees used to fit the model alpha: the weights of the trees used in the final aggregate model (AdaBoost only; see references for more information) F : F[[1]] corresponds to the training sum, F[[2]]], ... corresponds to testing sums. errs : matrix of errs, training, kappa, testing 1, kappa 1, ... lw : last weights calculated, used by update routine |

`fit` |
The predicted classification for each observation in the orginal level of the response. |

`call` |
The function call. |

`nu` |
shrinakge parameter |

`type` |
The type of adaboost performed: ‘discrete’, ‘real’, ‘logit’, and ‘gentle’. |

`confusion` |
The confusion matrix (True value vs. Predicted value) for the training data. |

`iter` |
The number of boosting iterations that were performed. |

`actual` |
The original response vector. |

### Warnings

For LogitBoost and Gentle Boost, under certain circumstances, the methods will fail to classify the data into more than one category. If this occurs, try modifying the rpart.control options such as ‘minsplit’, ‘cp’, and ‘maxdepth’.

‘ada’ does not currently handle multiclass problems. However, there is an example in (Culp et al., 2006) that shows how to use this code in that setting. Plots and other functions are not set up for this analysis.

### Author(s)

Mark Culp, University of Michigan Kjell Johnson, Pfizer, Inc. George Michailidis, University of Michigan

Special thanks goes to: Zhiguang Qian, Georgia Tech University Greg Warnes, Pfizer, Inc.

### References

Friedman, J. (1999). *Greedy Function Approximation: A Gradient Boosting Machine.*
Technical Report, Department of Statistics, Standford University.

Friedman, J., Hastie, T., and Tibshirani, R. (2000). *Additive Logistic Regression:
A statistical view of boosting*. Annals of Statistics, 28(2), 337-374.

Friedman, J. (2002). *Stochastic Gradient Boosting*.
Coputational Statistics \& Data Analysis 38.

Culp, M., Johnson, K., Michailidis, G. (2006). *ada: an R Package
for Stochastic Boosting* Journal of Statistical Software, 16.

### See Also

`print.ada`

,`summary.ada`

,`predict.ada`

`plot.ada`

,`pairs.ada`

,`update.ada`

`addtest`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
## fit discrete ada boost to a simple example
data(iris)
##drop setosa
iris[iris$Species!="setosa",]->iris
##set up testing and training data (60% for training)
n<-dim(iris)[1]
trind<-sample(1:n,floor(.6*n),FALSE)
teind<-setdiff(1:n,trind)
iris[,5]<- as.factor((levels(iris[,5])[2:3])[as.numeric(iris[,5])-1])
##fit 8-split trees
gdis<-ada(Species~.,data=iris[trind,],iter=20,nu=1,type="discrete")
##add testing data set
gdis=addtest(gdis,iris[teind,-5],iris[teind,5])
##plot gdis
plot(gdis,TRUE,TRUE)
##variable selection plot
varplot(gdis)
##pairwise plot
pairs(gdis,iris[trind,-5],maxvar=2)
##for many more examples refer to reference (Culp et al., 2006)
``` |

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