# Covariance-regularized regression, aka the Scout.

### Description

The main function of the "scout" package. Performs covariance-regularized regression. Required inputs are an x matrix of features (the columns are the features) and a y vector of observations. By default, Scout(2,1) is performed; however, $p_1$ and $p_2$ can be specified (in which case Scout($p_1$, $p_2$) is performed). Also, by default Scout is performed over a grid of lambda1 and lambda2 values, but a different grid of values (or individual values, rather than an entire grid) can be specified.

### Usage

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### 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) |

`newx` |
An *optional* argument, consisting of a matrix with ncol(x) columns, at which one wishes to make predictions for each (lam1,lam2) pair. |

`p1` |
The $L_p$ penalty for the covariance regularization. Must be one of 1, 2, or NULL. NULL corresponds to no covariance regularization. WARNING: When p1=1, and ncol(x)>500, Scout can be SLOW. We recommend that for very large data sets, you use Scout with p1=2. Also, when ncol(x)>nrow(x) and p1=1, then very small values of lambda1 (lambda1 < 1e-4) will cause problems with graphical lasso, and so those values will be automatically increased to 1e-4. |

`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). |

`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 covariance 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. |

`rescale` |
Should coefficients beta obtained by covariance-regularized regression be re-scaled by a constant, given by regressing $y$ onto $x beta$? This is done in Witten and Tibshirani (2008) and is important for good performance. Default is TRUE. |

`trace` |
Print out progress? Prints out each time a lambda1 is completed. This is a good idea, especially when ncol(x) is large. |

`standardize` |
Should the columns of x be scaled to have standard deviation 1, and should y be scaled to have standard deviation 1, before covariance-regularized regression is performed? This affects the meaning of the penalties that are applied. In general, standardization should be performed. Default is TRUE. |

### Value

`intercepts` |
Returns a matrix of intercepts, of dimension length(lam1s)xlength(lam2s) |

`coefficients` |
Returns an array of coefficients, of dimension length(lam1s)xlength(lam2s)xncol(x). |

`p1` |
p1 value used |

`p2` |
p2 value used |

`lam1s` |
lam1s used |

`lam2s` |
lam2s used |

### Note

When p1=1 and ncol(x)>500 or so, then Scout can be very slow!! Please use p1=2 when ncol(x) is large.

### 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

predict.scoutobject, cv.scout

### Examples

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