# Tuning parameters (ncomp, lambda.l1) for Adaptive Sparse PLS regression for continuous response, by K-fold cross-validation

### Description

The function `rirls.spls.tune`

tuns the hyper-parameter values used in the
`spls.adapt`

procedure, by minimizing the mean squared error of prediction over the
hyper-parameter grid, using Durif et al. (2015) adaptive SPLS algorithm.

### Usage

1 2 3 |

### Arguments

`X` |
a (n x p) data matrix of predictors. |

`Y` |
a (n) vector of (continuous) responses. |

`lambda.l1.range` |
a vecor of positive real values, in [0,1]. |

`ncomp.range` |
a vector of positive integers. |

`weight.mat` |
a (n x n) matrix used to weight the l2 metric in observation spase if necessary, especially the covariance inverse of the Ytrain observations in heteroskedastic context. If NULL, the l2 metric is the standard one, corresponding to homoskedastic model. |

`adapt` |
a boolean value, indicating whether the sparse PLS selection step sould be adaptive or not. |

`center.X` |
a boolean value indicating whether the design matrices Xtrain in train set and Xtest in test set if non NULL should be centered or not |

`scale.X` |
a boolean value indicating whether the design matrices Xtrain in train set and Xtest in test set if non NULL should be scaled or not, scale.X=TRUE implies center.X=TRUE |

`center.Y` |
a boolean value indicating whether the response Ytrain in train set should be centered or not |

`scale.Y` |
a boolean value indicating whether the response Ytrain should be scaled or not, scale.Y=TRUE implies center.Y=TRUE |

`weighted.center` |
a boolean value indicating whether should the centering take into account the weighted l2 metric or not (if TRUE, it implies that weighted.mat is non NULL). |

`return.grid` |
a boolean values indicating whether the grid of hyper-parameters values with corresponding mean prediction error rate over the folds should be returned or not. |

`ncores` |
a positve integer, indicating if the cross-validation procedure should be parallelized over the folds (ncores > nfolds would lead to the generation of unused child process). If ncores>1, the procedure generates ncores child process over the cpu corresponding number of cpu cores (see details). |

`nfolds` |
a positive integer indicating the number of folds in K-folds cross-validation procedure, nfolds=n corresponds to leave-one-out cross-validation. |

### Details

The columns of the data matrices `Xtrain`

and `Xtest`

may not be standardized,
since standardizing is can be performed by the function `spls.adapt.tune`

as a
preliminary step before the algorithm is run.

The procedure is described in Durif et al. (2015). The K-fold cross-validation can be summarize as follow: the train set is partitioned into K folds, for each value of hyper- parameters the model is fit K times, using each fold to compute the prediction error rate, and fitting the model on the remaining observations. The cross-validation procedure returns the optimal hyper-parameters values, meaning the one that minimize the mean squared error of prediction averaged over all the folds.

This procedures uses the `mclapply`

from the `parallel`

package, available on
GNU/Linux and MacOS. Users of Microsoft Windows can refer to the README file in the source to
be able to use a mclapply type function.

### Value

A list with the following components:

`lambda.l1.opt` |
the optimal value in |

`ncomp.opt` |
the optimal value in |

`cv.grid` |
the grid of hyper-parameters and corresponding prediction error rate over
the nfolds. |

### Author(s)

Ghislain Durif (http://lbbe.univ-lyon1.fr/-Durif-Ghislain-.html).

### References

G. Durif, F. Picard, S. Lambert-Lacroix (2015). Adaptive sparse PLS for logistic regression, (in prep), available on (http://arxiv.org/abs/1502.05933).

Chun, H., & Keles, S. (2010). Sparse partial least squares regression for simultaneous dimension reduction and variable selection. Journal of the Royal Statistical Society. Series B (Methodological), 72(1), 3-25. doi:10.1111/j.1467-9868.2009.00723.x

Chung, D., & Keles, S. (2010). Sparse partial least squares classification for high dimensional data. Statistical Applications in Genetics and Molecular Biology, 9, Article17. doi:10.2202/1544-6115.1492

### See Also

`spls.adapt`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
### load plsgenomics library
library(plsgenomics)
### generating data
n <- 100
p <- 1000
sample1 <- sample.cont(n=100, p=1000, kstar=20, lstar=2, beta.min=0.25, beta.max=0.75, mean.H=0.2,
sigma.H=10, sigma.F=5, sigma.E=5)
X <- sample1$X
Y <- sample1$Y
### tuning the hyper-parameters
cv1 <- spls.adapt.tune(X=X, Y=Y, lambda.l1.range=seq(0.05, 0.95, by=0.3), ncomp.range=1:2,
weight.mat=NULL, adapt=TRUE, center.X=TRUE,
center.Y=TRUE, scale.X=TRUE, scale.Y=TRUE, weighted.center=FALSE,
return.grid=TRUE, ncores=1, nfolds=10)
str(cv1)
### otpimal values
cv1$lambda.l1.opt
cv1$ncomp.opt
``` |

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