# Bolasso model.

### Description

This function performs a Bolasso logistic regression model and produces an optimal set of predictors.

### Usage

1 | ```
Bolasso(x, y, BM = 100, kfold = 10, seed = 0123)
``` |

### Arguments

`x` |
predictor matrix. |

`y` |
response variable, a factor object with values of 0 and 1. |

`BM` |
the number of bootstrapping, with the default value 100. |

`kfold` |
the number of folds of cross validation - default is 10. Although kfold can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is kfold=3. |

`seed` |
the seed for random sampling, with the default value 0123. |

### Details

This function runs the LASSO logistic regression model using several bootstrap samples of the original data, and then intersects the non-zero coefficients for estimating consistent coefficients. A specific value of BM parameter should be supplied, however BM=100 is proposed by default. Users can reduce the running time by using 3-fold CV, but the proposed 10-fold CV is assumed by default.

### Value

`BM` |
the number of bootstrapping in this procedure. |

`var.selected` |
significant variables that are selected by the Bolasso model. |

### References

[1] Friedman, J., Hastie, T. and Tibshirani, R. (2008). Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 33(1), 1-22.

[2] Bach, F.R. (2008). Bolasso: model consistent lasso estimation through the bootstrap. Proceedings of the 25th international conference on Machine learning. ACM. pp. 33:40.

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
library(datasets)
head(iris)
X <- as.matrix(subset(iris, iris$Species!="setosa")[, -5])
Y <- as.factor(ifelse(subset(iris, iris$Species!="setosa")[, 5]=='versicolor', 0, 1))
# Fit a Bolasso logistic regression model
# The BM parameter in the following example is set as small value to reduce
# the running time, however the default value is proposed
Bolasso.fit <- Bolasso(x=X, y=Y, BM=5, seed=0123)
# Significant variables that are selected by the Bolasso model
Bolasso.fit$var.selected
``` |