# Stability Approach to Regularization Selection for Lasso

### Description

Implements the Stability Approach to Regularization Selection (StARS) for Lasso

### Usage

1 2 3 | ```
lasso.stars(x, y, rep.num = 20, lambda = NULL, nlambda = 100,
lambda.min.ratio = 0.001, stars.thresh = 0.1, sample.ratio = NULL,
alpha = 1, verbose = TRUE)
``` |

### Arguments

`x` |
The |

`y` |
The |

`rep.num` |
The number of subsampling for StARS. The default value is |

`lambda` |
A sequence of decresing positive numbers to control regularization. Typical usage is to leave the input |

`nlambda` |
The number of regularization paramters. The default value is |

`lambda.min.ratio` |
The smallest value for |

`stars.thresh` |
The threshold of the variability in StARS. The default value is |

`sample.ratio` |
The subsampling ratio. The default value is |

`alpha` |
The tuning parameter for the elastic-net regression. The default value is |

`verbose` |
If |

### Details

StARS selects the optimal regularization parameter based on the variability of the solution path. It chooses the least sparse graph among all solutions with the same variability. An alternative threshold `0.05`

is chosen under the assumption that the model is correctly specified. In applications, the model is usually an approximation of the true model, `0.1`

is a safer choice. The implementation is based on the popular package "glmnet".

### Value

An object with S3 class "stars" is returned:

`path` |
The solution path of regression coefficients (in an |

`lambda` |
The regularization parameters used in Lasso |

`opt.index` |
The index of the optimal regularization parameter. |

`opt.beta` |
The optimal regression coefficients. |

`opt.lambda` |
The optimal regularization parameter. |

`Variability` |
The variability along the solution path. |

### Note

This function can only work under the setting when `d>1`

### Author(s)

Tuo Zhao Maintainers: Tuo Zhao <tourzhao@gmail.edu>

### References

1.Han Liu, Kathryn Roeder and Larry Wasserman. Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models. *Advances in Neural Information Processing Systems*, 2010.

2.Jerome Friedman, Trevor Hastie and Rob Tibshirani. Regularization Paths for Generalized Linear Models via Coordinate Descent. *Journal of Statistical Software*, Vol.33, No.1, 2008.

### See Also

`SML-package`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
#generate data
x = matrix(rnorm(50*80),50,80)
beta = c(3,2,1.5,rep(0,77))
y = rnorm(50) + x%*%beta
#StARS for Lasso
z1 = lasso.stars(x,y)
summary(z1)
plot(z1)
#StARS for Lasso
z2 = lasso.stars(x,y, stars.thresh = 0.05)
summary(z2)
plot(z2)
#StARS for Lasso
z3 = lasso.stars(x,y,rep.num = 50)
summary(z3)
plot(z3)
``` |