stars_coglasso {coglasso}

Stability selection of the best coglasso network

Description

stars_coglasso() selects the combination of hyperparameters given to coglasso() yielding the most stable, yet sparse network. Stability is computed upon network estimation from 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

stars_coglasso(
  coglasso_obj,
  stars_thresh = 0.1,
  stars_subsample_ratio = NULL,
  rep_num = 20,
  max_iter = 10,
  verbose = TRUE
)

Arguments

coglasso_obj

The object returned by coglasso().

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.

Details

StARS for collaborative graphical regression is an adaptation 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. In particular, two of these are penalty parameters with a direct influence on network sparsity, hence on stability. For every c parameter, stars_coglasso() explores one of the two penalty parameters (\lambda_w or \lambda_b), keeping the other one fixed at its previous best estimate, using the normal, one-dimentional StARS approach, until finding the best couple. It then selects the c parameter for which the best (\lambda_w, \lambda_b) couple yielded the most stable, yet sparse network.

Value

stars_coglasso() returns a list containing the results of the selection procedure, built upon the list returned by coglasso().

• ... are the same elements returned by coglasso().

• merge_lw and merge_lb are lists with as many elements as the number of c parameters explored. Every element is in turn a list of as many matrices as the number of \lambda_w (or \lambda_b) values explored. Each matrix is the "merged" adjacency matrix, the average of all the adjacency matrices estimated for those specific c and \lambda_w (or \lambda_b) values across all the subsampling in the last path explored before convergence, the one when the final combination of \lambda_w and \lambda_b is selected for the given c value.

• variability_lw and variability_lb are lists with as many elements as the number of c parameters explored. Every element is a numeric vector of as many items as the number of \lambda_w (or \lambda_b) values explored. Each item is the variability of the network estimated for those specific c and \lambda_w (or \lambda_b) values in the last path explored before convergence, the one when the final combination of \lambda_w and \lambda_b is selected for the given c value.

• opt_adj is a list of the adjacency matrices finally selected for each c parameter explored.

• opt_variability is a numerical vector containing the variabilities associated to the adjacency matrices in opt_adj.

• opt_index_lw and opt_index_lb are integer vectors containing the index of the selected \lambda_ws (or \lambda_bs) for each c parameters explored.

• opt_lambda_w and opt_lambda_b are vectors containing the selected \lambda_ws (or \lambda_bs) for each c parameters explored.

• sel_index_c, sel_index_lw and sel_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 and sel_lambda_b are the final selected parameters 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_density is the density of the final selected network.

• sel_icov is the inverse covariance matrix of the final selected network.

Examples

cg <- coglasso(multi_omics_sd_micro, pX = 4, nlambda_w = 3, nlambda_b = 3, nc = 3, verbose = FALSE)

# Takes around 20 seconds
sel_cg <- stars_coglasso(cg, verbose = FALSE)