xstars()
selects the combination of hyperparameters given to
coglasso()
yielding the most stable, yet sparse network. Stability is
computed upon network estimation from multiple subsamples of the multi-omics data set,
allowing repetition. Subsamples are collected for a fixed amount of times
(rep_num
), and with a fixed proportion of the total number of samples
(stars_subsample_ratio
).
Usage
xstars(
coglasso_obj,
stars_thresh = 0.1,
stars_subsample_ratio = NULL,
rep_num = 20,
max_iter = 10,
verbose = TRUE
)
Arguments
- coglasso_obj
The object of
S3
classcoglasso
returned bycoglasso()
.- stars_thresh
The threshold set for variability of the explored networks at each iteration of the algorithm. The \(\lambda_w\) or the \(\lambda_b\) associated to the most stable network before the threshold is overcome is selected.
- stars_subsample_ratio
The proportion of samples in the multi-omics data set to be randomly subsampled to estimate the variability of the network under the given hyperparameters setting. Defaults to 80% when the number of samples is smaller than 144, otherwise it defaults to \(\frac{10}{n}\sqrt{n}\).
- rep_num
The amount of subsamples of the multi-omics data set used to estimate the variability of the network under the given hyperparameters setting. Defaults to 20.
- max_iter
The greatest number of times the algorithm is allowed to choose a new best \(\lambda_w\). Defaults to 10.
- verbose
Print information regarding the progress of the selection procedure on the console.
Value
xstars()
returns an object of S3
class select_coglasso
containing the results of the
selection procedure, built upon the object of S3
class coglasso
returned by coglasso()
.
... are the same elements returned by
coglasso()
.merge
is the "merged" adjacency matrix, the average of all the adjacency matrices estimated across all the different subsamples for the selected combination of \(\lambda_w\), \(\lambda_b\), and \(c\) values in the last path explored before convergence. Each entry is a measure of how recurrent the corresponding edge is across the subsamples.variability_lw
,variability_lb
andvariability_c
are numeric vectors of as many items as the number of \(\lambda_w\), \(\lambda_b\), and \(c\) values explored. Each item is the variability of the network estimated for the corresponding hyperparameter value, keeping the other two hyperparameters fixed to their selected value.sel_index_c
,sel_index_lw
andsel_index_lb
are the indexes of the final selected parameters \(c\), \(\lambda_w\) and \(\lambda_b\) leading to the most stable sparse network.sel_c
,sel_lambda_w
andsel_lambda_b
are the final selected hyperparameters \(c\), \(\lambda_w\) and \(\lambda_b\) leading to the most stable sparse network.sel_adj
is the adjacency matrix of the final selected network.sel_variability
is the variability of the final selected network.sel_density
is the density of the final selected network.sel_icov
is the inverse covariance matrix of the final selected network.sel_cov
optional, given only whencoglasso()
was called withcov_output = TRUE
. It is the covariance matrix associated with the final selected network.call
is the matched call.method
is the chosen model selection method. Here, it is "xstars".
Details
eXtended StARS (XStARS) is an adaptation for collaborative graphical regression of the method
published by Liu, H. et al. (2010): Stability Approach to Regularization
Selection (StARS). StARS was developed for network estimation regulated by
a single penalty parameter, while collaborative graphical lasso needs to
explore three different hyperparameters. These all have, to a different
degree, a direct influence on network sparsity, hence on stability. For every
iteration, xstars()
explores one of the three parameters (\(\lambda_w\),
\(\lambda_b\), or \(c\)), keeping the other ones fixed at their previous
selected estimate, using the normal, one-dimentional StARS approach, until
finding the best combination of the three that yields the most stable, yet
sparse network.