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Select the best coglasso network

Source: R/select_coglasso.R
select_coglasso.Rd

select_coglasso() selects the best combination of hyperparameters given to coglasso() according to the selected model selection method. The three availble options that can be set for the argument method are "xstars", "xestars" and "ebic".

Usage

select_coglasso(
  coglasso_obj,
  method = "xestars",
  stars_thresh = 0.1,
  stars_subsample_ratio = NULL,
  rep_num = 20,
  max_iter = 10,
  old_sampling = FALSE,
  light = TRUE,
  ebic_gamma = 0.5,
  verbose = TRUE
)

Arguments

coglasso_obj

The object of S3 class coglasso returned by coglasso().

method

The model selection method to select the best combination of hyperparameters. The available options are "xstars", "xestars" and "eBIC". Defaults to "xestars".

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.

old_sampling

Perform the same subsampling xstars() would if set to TRUE. Makes a difference with bigger data sets, where computing a correlation matrix could take significantly longer. Defaults to FALSE.

light

Do not store the "merged" matrixes recording average variability of each edge, making the algorithm more memory efficient, if set to TRUE. Defaults to TRUE.

ebic_gamma

The \(\gamma\) tuning parameter for eBIC selection, to set between 0 and 1. When set to 0 one has the standard BIC. Defaults to 0.5.

verbose

Print information regarding the progress of the selection procedure on the console.

Value

select_coglasso() returns an object of S3 class select_coglasso containing the results of the selection procedure, built upon an object of S3 class coglasso. Some output elements depend on the chosen model selection method.
These elements are returned by all methods:

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

  • 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.

  • call is the matched call.

  • method is the chosen model selection method.

These are the additional elements returned when choosing "xestars":

  • 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 \(\lambda_w\)s (or \(\lambda_b\)s) for each \(c\) parameters explored.

  • opt_lambda_w and opt_lambda_b are vectors containing the selected \(\lambda_w\)s (or \(\lambda_b\)s) for each \(c\) parameters explored.

  • merge_lw and merge_lb are returned only if light is set to FALSE. They are lists with as many elements as the number of \(c\) parameters explored. Every element is a "merged" adjacency matrix, the average of all the adjacency matrices estimated for those specific \(c\) and the selected \(\lambda_w\) (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.

These are the additional elements returned when choosing "xstars":

  • 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 \(\lambda_w\)s (or \(\lambda_b\)s) for each \(c\) parameters explored.

  • opt_lambda_w and opt_lambda_b are vectors containing the selected \(\lambda_w\)s (or \(\lambda_b\)s) for each \(c\) parameters explored.

These are the additional elements returned when choosing "ebic":

  • ebic_scores is a numerical vector containing the eBIC scores for all the hyperparameter combination.

Details

select_coglasso() provides three model selection strategies:

  • "xstars" uses eXtended StARS (XStARS) selecting 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). See xstars() for more information on the methodology.

  • "xestars" uses eXtended Efficient StARS (XEStARS), a significantly faster and memory-effcient version of XStARS. It could produce marginally different results to "xstars" due to a different sampling strategy. See xestars() for more information on the methodology.

  • "ebic" uses the extended Bayesian Information Criterion (eBIC) selecting the network that minimizes it. gamma sets the wait given to the extended component, turning the model selection method to the standard BIC if set to 0.

Examples

cg <- coglasso(multi_omics_sd_micro, p = c(4, 2), nlambda_w = 3, 
               nlambda_b = 3, nc = 3, verbose = FALSE)
# Using eXtended Efficient StARS, takes less than five seconds
sel_cg_xestars <- select_coglasso(cg, method = "xestars", verbose = FALSE)
# \donttest{
# Using eXtended StARS, takes around a minute
sel_cg_xstars <- select_coglasso(cg, method = "xstars", verbose = FALSE)
# }
# Using eBIC
sel_cg_ebic <- select_coglasso(cg, method = "ebic", verbose = FALSE)