stability.selection {plsgenomics}

Stability selection procedure to select covariates for the sparse PLS, LOGIT-SPLS and multinomial-SPLS methods

Description

The function stability.selection returns the list of selected covariates, when following the stability selection procedure described in Durif et al. (2018). In particular, it selects covariates that are selected by most of the sparse PLS, the logit-SPLS or the multinomial-SPLS models when exploring the grid of hyper-parameter candidate values.

Usage

stability.selection(stab.out, piThreshold = 0.9, rhoError = 10)

Arguments

stab.out

the output of the functions spls.stab, logit.spls.stab or multinom.spls.stab.

piThreshold

a value in (0,1], corresponding to the threshold probability used to select covariate (c.f. Durif et al., 2018).

rhoError

a positive value used to restrict the grid of hyper-parameter candidate values (c.f. Durif et al., 2018).

Details

The procedure is described in Durif et al. (2018). The stability selection procedure can be summarize as follow (c.f. Meinshausen and Buhlmann, 2010).

(i) For each candidate values of hyper-parameters, a model is trained on nresamp resamplings of the data. Then, for each candidate value of the hyper-parameters, the probability that a covariate (i.e. a column in X) is selected is computed among the resamplings.

The estimated probabilities can be visualized as a heatmap with the function stability.selection.heatmap.

(ii) Eventually, the set of "stable selected" variables corresponds to the set of covariates that were selected by most of the training among the grid of hyper-parameters candidate values, based on a threshold probability piThreshold and a restriction of the grid of hyper-parameters based on rhoError (c.f. Durif et al., 2018, for details).

This function achieves the second step (ii) of the stability selection procedure. The first step (i) is achieved by the functions spls.stab, logit.spls.stab or multinom.spls.stab.

Value

An object with the following attributes:

selected.predictors

The list of the name of covariates that are selected.

max.probs

The corresponding estimated probabilities of selection for each covariate, i.e. the maximal values on the reduced grid of hyper-parameters.

Author(s)

Ghislain Durif (https://gdurif.perso.math.cnrs.fr/).

References

Durif, G., Modolo, L., Michaelsson, J., Mold, J.E., Lambert-Lacroix, S., Picard, F., 2018. High dimensional classification with combined adaptive sparse PLS and logistic regression. Bioinformatics 34, 485–493. doi:10.1093/bioinformatics/btx571. Available at http://arxiv.org/abs/1502.05933.

Meinshausen, N., Buhlmann P. (2010). Stability Selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72, no. 4, 417-473.

See Also

spls.stab, logit.spls.stab, multinom.spls.stab, stability.selection.heatmap

Examples

## Not run: 
### load plsgenomics library
library(plsgenomics)

### generating data
n <- 100
p <- 100
sample1 <- sample.cont(n=n, p=p, kstar=10, 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

### hyper-parameters values to test
lambda.l1.range <- seq(0.05,0.95,by=0.1) # between 0 and 1
ncomp.range <- 1:10

### tuning the hyper-parameters
stab1 <- spls.stab(X=X, Y=Y, lambda.l1.range=lambda.l1.range, 
                   ncomp.range=ncomp.range, weight.mat=NULL, 
                   adapt=FALSE, center.X=TRUE, center.Y=TRUE, 
                   scale.X=TRUE, scale.Y=TRUE, weighted.center=FALSE, 
                   ncores=1, nresamp=100)
                       
str(stab1)

### selected covariates
stability.selection(stab1, piThreshold=0.6, rhoError=10)

## End(Not run)