Package 'coglasso'

Build multiple networks and select the best one from a multi-omics data set

Description

bs() wraps the two main functions of the package in a single one: coglasso(), to build multiple multi-omics networks, and select_coglasso() to select the best one according to the chosen criterion.

Usage

bs(
  data,
  p = NULL,
  pX = lifecycle::deprecated(),
  lambda_w = NULL,
  lambda_b = NULL,
  c = NULL,
  nlambda_w = NULL,
  nlambda_b = NULL,
  nc = NULL,
  lambda_w_max = NULL,
  lambda_b_max = NULL,
  c_max = NULL,
  lambda_w_min_ratio = NULL,
  lambda_b_min_ratio = NULL,
  c_min = NULL,
  icov_guess = NULL,
  cov_output = FALSE,
  lock_lambdas = FALSE,
  method = "xestars",
  stars_thresh = 0.1,
  stars_subsample_ratio = NULL,
  rep_num = 20,
  max_iter = 10,
  old_sampling = FALSE,
  ebic_gamma = 0.5,
  verbose = TRUE
)

Arguments

data	The input multi-omics data set. Rows should be samples, columns should be variables. Variables should be grouped by their assay (e.g. transcripts first, then metabolites). data is a required parameter.
p	A vector with with the number of variables for each omic layer of the data set (e.g. the number of transcripts, metabolites etc.), in the same order the layers have in the data set. If given a single number, coglasso() assumes that the total of data sets is two, and that the number given is the dimension of the first one.
pX	pX is no longer supported. Please use p.
lambda_w	A vector of values for the parameter $\lambda_w$, the penalization parameter for the "within" interactions. Overrides nlambda_w.
lambda_b	A vector of values for the parameter $\lambda_b$, the penalization parameter for the "between" interactions. Overrides nlambda_b.
c	A vector of values for the parameter $c$, the weight given to collaboration. Overrides nc.
nlambda_w	The number of requested $\lambda_w$ parameters to explore. A sequence of size nlambda_w of $\lambda_w$ parameters will be generated. Defaults to 8. Ignored when lambda_w is set by the user.
nlambda_b	The number of requested $\lambda_b$ parameters to explore. A sequence of size nlambda_b of $\lambda_b$ parameters will be generated. Defaults to 8. Ignored when lambda_b is set by the user.
nc	The number of requested $c$ parameters to explore. A sequence of size nc of $c$ parameters will be generated. Defaults to 5. Ignored when c is set by the user.
lambda_w_max	The greatest generated $\lambda_w$. By default it is computed with a data-driven approach. Ignored when lambda_w is set by the user.
lambda_b_max	The greatest generated $\lambda_b$. By default it is computed with a data-driven approach. Ignored when lambda_b is set by the user.
c_max	The greatest $c$ explored. Defaults to 100. Ignored when c is set by the user.
lambda_w_min_ratio	The ratio of the smallest generated $\lambda_w$ over the greatest generated $\lambda_w$. Defaults to 0.1. Ignored when lambda_w is set by the user.
lambda_b_min_ratio	The ratio of the smallest generated $\lambda_b$ over the greatest generated $\lambda_b$. Defaults to 0.1. Ignored when lambda_b is set by the user.
c_min	The the smallest $c$ explored. Defaults to $\frac{1}{c_{max}}$, so to 0.01 if c_max is not set by the user. Ignored when c is set by the user.
icov_guess	Use a predetermined inverse covariance matrix as an initial guess for the network estimation.
cov_output	Add the estimated variance-covariance matrix to the output.
lock_lambdas	Set $\lambda_w = \lambda_b$. Force a single lambda parameter for both "within" and "between" interactions.
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.
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 network building and the network selection processes.

Details

When using bs(), first, coglasso() estimates multiple multi-omics networks with the algorithm collaborative graphical lasso, one for each combination of input values for the hyperparameters $\lambda_w$, $\lambda_b$ and $c$. Then, 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". For more information on these selection methods, visit the help page of select_coglasso().

Value

bs() returns an object of S3 class select_coglasso containing several elements. The most important is probably sel_adj, the adjacency matrix of the selected network. Some output elements depend on the chosen model selection method.
These elements are always returned, and they are the result of network estimation with coglasso():

• loglik is a numerical vector containing the $log$ likelihoods of all the estimated networks.

• density is a numerical vector containing a measure of the density of all the estimated networks.

• df is an integer vector containing the degrees of freedom of all the estimated networks.

• convergence is a binary vector containing whether a network was successfully estimated for the given combination of hyperparameters or not.

• path is a list containing the adjacency matrices of all the estimated networks.

• icov is a list containing the inverse covariance matrices of all the estimated networks.

• nexploded is the number of combinations of hyperparameters for which coglasso() failed to converge.

• data is the input multi-omics data set.

• hpars is the ordered table of all the combinations of hyperparameters given as input to bs(), with $\alpha(\lambda_w+\lambda_b)$ being the key to sort rows.

• lambda_w, lambda_b, and c are numerical vectors with, respectively, all the $\lambda_w$, $\lambda_b$, and $c$ values bs() used.

• p is the vector with the number of variables for each omic layer of the data set.

• D is the number of omics layers in the data set.

• cov optional, returned when cov_output is TRUE, is a list containing the variance-covariance matrices of all the estimated networks.

These elements are returned by all selection methods available:

• 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.

• sel_cov optional, given only when coglasso() was called with cov_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.

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

• 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 and variability_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_variability is the variability of the final selected network.

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

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

Examples

# Suggested usage: give the input data set, set the values for `p` and the 
# number of hyperparameters to explore (to choose how extensively to explore 
# the possible hyperparameters). Then, let the default behavior do the rest:

sel_mo_net <- bs(multi_omics_sd_micro, p = c(4, 2), nlambda_w = 3, 
                 nlambda_b = 3, nc = 3, verbose = FALSE)

---

Estimate networks from a multi-omics data set

Description

coglasso() estimates multiple multi-omics networks with the algorithm collaborative graphical lasso, one for each combination of input values for the hyperparameters $\lambda_w$, $\lambda_b$ and $c$.

Usage

coglasso(
  data,
  p = NULL,
  pX = lifecycle::deprecated(),
  lambda_w = NULL,
  lambda_b = NULL,
  c = NULL,
  nlambda_w = NULL,
  nlambda_b = NULL,
  nc = NULL,
  lambda_w_max = NULL,
  lambda_b_max = NULL,
  c_max = NULL,
  lambda_w_min_ratio = NULL,
  lambda_b_min_ratio = NULL,
  c_min = NULL,
  icov_guess = NULL,
  cov_output = FALSE,
  lock_lambdas = FALSE,
  verbose = TRUE
)

Arguments

data	The input multi-omics data set. Rows should be samples, columns should be variables. Variables should be grouped by their assay (e.g. transcripts first, then metabolites). data is a required parameter.
p	A vector with with the number of variables for each omic layer of the data set (e.g. the number of transcripts, metabolites etc.), in the same order the layers have in the data set. If given a single number, coglasso() assumes that the total of data sets is two, and that the number given is the dimension of the first one.
pX	pX is no longer supported. Please use p.
lambda_w	A vector of values for the parameter $\lambda_w$, the penalization parameter for the "within" interactions. Overrides nlambda_w.
lambda_b	A vector of values for the parameter $\lambda_b$, the penalization parameter for the "between" interactions. Overrides nlambda_b.
c	A vector of values for the parameter $c$, the weight given to collaboration. Overrides nc.
nlambda_w	The number of requested $\lambda_w$ parameters to explore. A sequence of size nlambda_w of $\lambda_w$ parameters will be generated. Defaults to 8. Ignored when lambda_w is set by the user.
nlambda_b	The number of requested $\lambda_b$ parameters to explore. A sequence of size nlambda_b of $\lambda_b$ parameters will be generated. Defaults to 8. Ignored when lambda_b is set by the user.
nc	The number of requested $c$ parameters to explore. A sequence of size nc of $c$ parameters will be generated. Defaults to 5. Ignored when c is set by the user.
lambda_w_max	The greatest generated $\lambda_w$. By default it is computed with a data-driven approach. Ignored when lambda_w is set by the user.
lambda_b_max	The greatest generated $\lambda_b$. By default it is computed with a data-driven approach. Ignored when lambda_b is set by the user.
c_max	The greatest $c$ explored. Defaults to 100. Ignored when c is set by the user.
lambda_w_min_ratio	The ratio of the smallest generated $\lambda_w$ over the greatest generated $\lambda_w$. Defaults to 0.1. Ignored when lambda_w is set by the user.
lambda_b_min_ratio	The ratio of the smallest generated $\lambda_b$ over the greatest generated $\lambda_b$. Defaults to 0.1. Ignored when lambda_b is set by the user.
c_min	The the smallest $c$ explored. Defaults to $\frac{1}{c_{max}}$, so to 0.01 if c_max is not set by the user. Ignored when c is set by the user.
icov_guess	Use a predetermined inverse covariance matrix as an initial guess for the network estimation.
cov_output	Add the estimated variance-covariance matrix to the output.
lock_lambdas	Set $\lambda_w = \lambda_b$. Force a single lambda parameter for both "within" and "between" interactions.
verbose	Print information regarding current coglasso run on the console.

Value

coglasso() returns an object of S3 class coglasso, that has the following elements:

• loglik is a numerical vector containing the $log$ likelihoods of all the estimated networks.

• density is a numerical vector containing a measure of the density of all the estimated networks.

• df is an integer vector containing the degrees of freedom of all the estimated networks.

• convergence is a binary vector containing whether a network was successfully estimated for the given combination of hyperparameters or not.

• path is a list containing the adjacency matrices of all the estimated networks.

• icov is a list containing the inverse covariance matrices of all the estimated networks.

• nexploded is the number of combinations of hyperparameters for which coglasso() failed to converge.

• data is the input multi-omics data set.

• hpars is the ordered table of all the combinations of hyperparameters given as input to coglasso(), with $\alpha(\lambda_w+\lambda_b)$ being the key to sort rows.

• lambda_w is a numerical vector with all the $\lambda_w$ values coglasso() used.

• lambda_b is a numerical vector with all the $\lambda_b$ values coglasso() used.

• c is a numerical vector with all the $c$ values coglasso() used.

• p is the vector with the number of variables for each omic layer of the data set.

• D is the number of omics layers in the data set.

• icov_guess optional, returned when icov_guess is given. It is the predetermined inverse covariance matrix given by the user as an initial guess for the network estimation.

• cov optional, returned when cov_output is TRUE, is a list containing the variance-covariance matrices of all the estimated networks.

• call is the matched call.

Examples

# Typical usage: set the number of hyperparameters to explore
cg <- coglasso(multi_omics_sd_micro,
  p = c(4, 2), nlambda_w = 3,
  nlambda_b = 3, nc = 3, verbose = FALSE
)

# Model selection using eXtended Efficient StARS, takes less than five seconds
sel_cg_xestars <- select_coglasso(cg, method = "xestars", verbose = FALSE)

---

Extract a coglasso network

Description

get_network() extracts the selected network from a select_coglasso object, or a different specific one from either a select_coglasso or a coglasso object when specifying the optional parameters.

Usage

get_network(sel_cg_obj, index_c = NULL, index_lw = NULL, index_lb = NULL)

Arguments

sel_cg_obj	The object of S3 class select_coglasso or of S3 class coglasso.
index_c	The index of the $c$ value different from the one selected by model selection. To set only if the desired network is not the selected one.
index_lw	The index of the $\lambda_w$ value of the chosen non-optimal network. To set only if the desired network is not the selected one.
index_lb	The index of the $\lambda_b$ value of the chosen non-optimal network. To set only if the desired network is not the selected one.

Details

If the input is a coglasso object, it is necessary to specify all the indexes to extract the chosen network.
If the input is a select_coglasso object, it extracts by default the selected network. If the selection method was "ebic", and you want to extract a different network than the selected one, specify all indexes. Otherwise, if the objective is to extract the optimal network for a specific $c$ value different than the selected one, set index_c to your chosen one. Also here it is possible to extract a specific non-optimal network by setting all the indexes to the chosen ones.

Value

get_network() returns the selected network, in the form of an object of class igraph.

Examples

sel_cg <- bs(multi_omics_sd_micro, p = c(4, 2), nlambda_w = 3, nlambda_b = 3,
                 nc = 3, verbose = FALSE)
sel_net <- get_network(sel_cg)
# Could even plot the selected network with plot(sel_net), but then it would
# plot an unnotated network, better to directly plot(sel_cg).
print(sel_net)

---

Extract a coglasso partial correlation matrix

Description

get_pcor() extracts the selected partial correlation matrix from a select_coglasso object, or a different specific one from either a select_coglasso or a coglasso object when specifying the optional parameters.

Usage

get_pcor(sel_cg_obj, index_c = NULL, index_lw = NULL, index_lb = NULL)

Arguments

sel_cg_obj	The object of S3 class select_coglasso or of S3 class coglasso.
index_c	The index of the $c$ value different from the one selected by model selection. To set only if the desired partial correlation matrix is not the selected one.
index_lw	The index of the $\lambda_w$ value of the chosen non-optimal partial correlation matrix. To set only if the desired partial correlation matrix is not the selected one.
index_lb	The index of the $\lambda_b$ value of the chosen non-optimal partial correlation matrix. To set only if the desired partial correlation matrix is not the selected one.

Details

If the input is a coglasso object, it is necessary to specify all the indexes to extract the chosen partial correlation matrix.
If the input is a select_coglasso object, it extracts by default the selected partial correlation matrix. If the selection method was "ebic", and you want to extract a different partial correlation matrix than the selected one, specify all indexes. Otherwise, if the objective is to extract the optimal partial correlation matrix for a specific $c$ value different than the selected one, set index_c to your chosen one. Also here it is possible to extract a specific non-optimal partial correlation matrix by setting all the indexes to the chosen ones.

Value

get_pcor() returns the selected partial correlation matrix.

Examples

sel_cg <- bs(multi_omics_sd_micro, p = c(4, 2), nlambda_w = 3, nlambda_b = 3,
                 nc = 3, verbose = FALSE)
sel_pcor <- get_pcor(sel_cg)
print(sel_pcor)

---

Multi-omics dataset of sleep deprivation in mouse

Description

A dataset containing transcript and metabolite values analysed in Albanese et al. 2023, subset of the multi-omics data set published in Jan, M., Gobet, N., Diessler, S. et al. A multi-omics digital research object for the genetics of sleep regulation. Sci Data 6, 258 (2019).

multi_omics_sd_small is a smaller version, limited to the transcript Cirbp and the transcripts and metabolites belonging to its neighborhood as described in Albanese et al. 2023

multi_omics_sd_micro is a minimal version with Cirbp and a selection of its neighborhood.

Usage

multi_omics_sd

multi_omics_sd_small

multi_omics_sd_micro

Format

multi_omics_sd

A data frame with 30 rows and 238 variables (162 transcripts and 76 metabolites):

Plin4 to Tfrc

log2 CPM values of 162 transcripts in mouse cortex under sleep deprivation (-4.52–10.46)

Ala to SM C24:1

abundance values of 76 metabolites (0.02–1112.67)

multi_omics_sd_small

A data frame with 30 rows and 19 variables (14 transcripts and 5 metabolites)

Cirbp to Stip1

log2 CPM values of 14 transcripts in mouse cortex under sleep deprivation (4.24–9.31)

Phe to PC ae C32:2

Abundance values of 5 metabolites (0.17–145.33)

multi_omics_sd_micro

A data frame with 30 rows and 6 variables (4 transcripts and 2 metabolites)

Cirbp to Dnajb11

log2 CPM values of 4 transcripts in mouse cortex under sleep deprivation (4.78–9.31)

Trp to PC aa C36:3

Abundance values of 2 metabolites (58.80–145.33)

Source

Jan, M., Gobet, N., Diessler, S. et al. A multi-omics digital research object for the genetics of sleep regulation. Sci Data 6, 258 (2019) doi:10.1038/s41597-019-0171-x

Figshare folder of the original manuscript: https://figshare.com/articles/dataset/Input_data_for_systems_genetics_of_sleep_regulation/7797434

---

Plot selected coglasso networks

Description

plot.select_coglasso() creates an annotated plot of a coglasso selected network from an object of S3 class select_coglasso. Variables from different data sets will have different color coding. To plot the network, it's enough to use plot() call on the select_coglasso object.

plot.coglasso() has the same functioning as select_coglasso.plot(), but from an object of S3 class coglasso. In this case, it is compulsory to specify index_c, index_lw, and index_lb.

Usage

## S3 method for class 'select_coglasso'
plot(
  x,
  index_c = NULL,
  index_lw = NULL,
  index_lb = NULL,
  node_labels = TRUE,
  hide_isolated = TRUE,
  ...
)

## S3 method for class 'coglasso'
plot(
  x,
  index_c,
  index_lw,
  index_lb,
  node_labels = TRUE,
  hide_isolated = TRUE,
  ...
)

Arguments

x	The object of S3 class select_coglasso.
index_c	The index of the $c$ value different from the one selected by model selection. To set only if the desired network is not the selected one.
index_lw	The index of the $\lambda_w$ value of the chosen non-optimal network. To set only if the desired network is not the selected one.
index_lb	The index of the $\lambda_b$ value of the chosen non-optimal network. To set only if the desired network is not the selected one.
node_labels	Show node names in the network. Defaults to TRUE.
hide_isolated	Hide nodes that are not connected to any other node. Defaults to TRUE.
...	System required, not used here.

Details

If the input is a coglasso object, it is necessary to specify all the indexes to extract the chosen network.
If the input is a select_coglasso object, it extracts by default the selected network. If the selection method was "ebic", and you want to extract a different network than the selected one, specify all indexes. Otherwise, if the objective is to extract the optimal network for a specific $c$ value different than the selected one, set index_c to your chosen one. Also here it is possible to extract a specific non-optimal network by setting all the indexes to the chosen ones.

Value

Returns NULL, invisibly.

See Also

get_network() to understand what it means to select a specific network with index_c, index_lw, and index_lb.

Examples

sel_cg <- bs(multi_omics_sd_small, p = c(14, 5), nlambda_w = 15, nlambda_b = 15,
             nc = 3, lambda_w_min_ratio = 0.6, verbose = FALSE)
plot(sel_cg)

---

Select the best coglasso network

Description

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,
  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.
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.

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 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.

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.

• sel_cov optional, given only when coglasso() was called with cov_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.

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

• 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 and variability_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_variability is the variability of the final selected network.

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

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

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)

# 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)

---

Efficient stability selection of the best coglasso network

Description

xestars() provides a more efficient and lighter implementation than xstars() to select 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

xestars(
  coglasso_obj,
  stars_thresh = 0.1,
  stars_subsample_ratio = NULL,
  rep_num = 20,
  max_iter = 10,
  old_sampling = FALSE,
  verbose = TRUE
)

Arguments

coglasso_obj	The object of S3 class coglasso 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.
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.
verbose	Print information regarding the progress of the selection procedure on the console.

Details

eXtended Efficient StARS (XEStARS) is a more efficient and memory-light version of XStARS, the 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 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. What makes it more efficient than xstars() is the different way that the stability check is implemented in the two algorithms. In xstars() (and even in the original StARS), the stability check is performed, for example, for every $\lambda_w$ value (or $\lambda_b$, or $c$), until all values are explored, and then it when the algorithm selects the one yielding the most stable, yet sparse network, and only then switching to the selection of the following hyperparameter. In xestars(), the stability check becomes a stopping criterion. The moment that the stability threshold is passed, the value of the hyperparameter currently being selected is fixed, and the switch to the next one happens immediately, without exploring the whole landscape. This reduces sensibly the number of iterations before convergence to a final network.
The original XStARS computes a new subsampling for every time the algorithm switches from optimizing $\lambda_w$, $\lambda_b$, or $c$. This does not allow to compare the hyperparameters on an equal ground, and can slow the selection down with bigger data set or a larger hyperparameter space. To allow a similar subsampling to xstars(), the old_sampling parameter has been implemented. If set to TRUE, the subsampling is similar to the one xstars() would perform. Otherwise, the subsampling is performed at the beginning of the algorithm once and for all its iterations.

Value

xestars() 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 and variability_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 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_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 when coglasso() was called with cov_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 "xestars".

Examples

cg <- coglasso(multi_omics_sd_micro, p = c(4, 2), nlambda_w = 3, 
               nlambda_b = 3, nc = 3, verbose = FALSE)

# Takes less than five seconds
sel_cg <- xestars(cg, verbose = FALSE)

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Stability selection of the best coglasso network

Description

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 class coglasso 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

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.

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 and variability_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 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 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 when coglasso() was called with cov_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".

Examples

cg <- coglasso(multi_omics_sd_micro, p = c(4, 2), nlambda_w = 3, 
               nlambda_b = 3, nc = 3, verbose = FALSE)

# Takes around one minute
sel_cg <- xstars(cg, verbose = FALSE)

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