# Perform cross-validation for covariance-regularized regression, aka the Scout.

### Description

This function returns cross-validation error rates for a range of lambda1 and lambda2 values, and also makes beautiful CV plots if plot=TRUE.

### Usage

1 2 3 |

### Arguments

`x` |
A matrix of predictors, where the rows are the samples and the columns are the predictors |

`y` |
A matrix of observations, where length(y) should equal nrow(x) |

`K` |
Number of cross-validation folds to be performed; default is 10 |

`lam1s` |
The (vector of) tuning parameters for regularization of the covariance matrix. Can be NULL if p1=NULL, since then no covariance regularization is taking place. If p1=1 and nrow(x)<ncol(x), then the no value in lam1s should be smaller than 1e-3, because this will cause graphical lasso to take too long. Also, if ncol(x)>500 then we really do not recommend using p1=1, as graphical lasso can be uncomfortably slow. |

`lam2s` |
The (vector of) tuning parameters for the $L_1$ regularization of the regression coefficients, using the regularized covariacne matrix. Can be NULL if p2=NULL. (If p2=NULL, then non-zero lam2s have no effect). A value of 0 will result in no regularization. |

`p1` |
The $L_p$ penalty for the covariance regularization. Must be one of 1, 2, or NULL. NULL corresponds to no covariance regularization. |

`p2` |
The $L_p$ penalty for the estimation of the regression coefficients based on the regularized covariance matrix. Must be one of 1 (for $L_1$ regularization) or NULL (for no regularization). |

`trace` |
Print out progress as we go? Default is TRUE. |

`plot` |
If TRUE (by default), makes beautiful CV plots. |

`plotSE` |
Should those beautiful CV plots also display std error bars for the CV? Default is FALSE |

`rescale` |
Scout rescales coefficients, by default, in order to avoid over-shrinkage |

`...` |
Additional parameters |

### Details

Pass in a data matrix x and a vector of outcomes y; it will perform (10-fold) cross-validation over a range of lambda1 and lambda2 values. By default, Scout(2,1) is performed.

### Value

`folds` |
The indices of the members of the K test sets are returned. |

`cv` |
A matrix of average cross-validation errors is returned. |

`cv.error` |
A matrix containing the standard errors of the elements in "cv", the matrix of average cross-validation errors. |

`bestlam1` |
Best value of lam1 found via cross-validation. |

`bestlam2` |
Best value fo lam2 found via cross-validation. |

`lam1s` |
Values of lam1 considered. |

`lam2s` |
Values of lam2 considered. |

### Author(s)

Daniela M. Witten and Robert Tibshirani

### References

Witten, DM and Tibshirani, R (2008) Covariance-regularized regression and classification for high-dimensional problems. Journal of the Royal Statistical Society, Series B 71(3): 615-636. <http://www-stat.stanford.edu/~dwitten>

### See Also

scout, predict.scoutobject

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
library(lars)
data(diabetes)
attach(diabetes)
par(mfrow=c(2,1))
par(mar=c(2,2,2,2))
## Not run: cv.sc <- cv.scout(x2,y,p1=2,p2=1)
## Not run: print(cv.sc)
## Not run: cv.la <- cv.lars(x2,y)
## Not run: print(c("Lars minimum CV is ", min(cv.la$cv)))
## Not run: print(c("Scout(2,1) minimum CV is ", min(cv.sc$cv)))
detach(diabetes)
``` |

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