Runs stability selection graphical models with different combinations of parameters controlling the sparsity of the underlying selection algorithm (e.g. penalty parameter for regularised models) and thresholds in selection proportions. These two parameters are jointly calibrated by maximising the stability score of the model (possibly under a constraint on the expected number of falsely stably selected features). This function uses a serial implementation and requires the grid of parameters controlling the underlying algorithm as input (for internal use only).
SerialGraphical(
xdata,
pk = NULL,
Lambda,
lambda_other_blocks = 0.1,
pi_list = seq(0.6, 0.9, by = 0.01),
K = 100,
tau = 0.5,
seed = 1,
n_cat = n_cat,
implementation = PenalisedGraphical,
start = "cold",
scale = TRUE,
resampling = "subsampling",
cpss = FALSE,
PFER_method = "MB",
PFER_thr = Inf,
FDP_thr = Inf,
output_data = FALSE,
verbose = TRUE,
...
)A list with:
a matrix of the best stability scores for different (sets of) parameters controlling the level of sparsity in the underlying algorithm.
a matrix of parameters controlling the level of sparsity in the underlying algorithm.
a matrix of the average number of selected features by the underlying algorithm with different parameters controlling the level of sparsity.
a matrix of the calibrated number of stably selected features with different parameters controlling the level of sparsity.
a matrix of calibrated thresholds in selection proportions for different parameters controlling the level of sparsity in the underlying algorithm.
a matrix of upper-bounds in PFER of calibrated stability selection models with different parameters controlling the level of sparsity.
a matrix of upper-bounds in FDP of calibrated stability selection models with different parameters controlling the level of sparsity.
a matrix of stability scores obtained with different combinations of parameters. Columns correspond to different thresholds in selection proportions.
a matrix of
upper-bounds in FDP obtained with different combinations of parameters.
Columns correspond to different thresholds in selection proportions. Only
returned if length(pk)=1.
a matrix of upper-bounds in
PFER obtained with different combinations of parameters. Columns correspond
to different thresholds in selection proportions. Only returned if
length(pk)=1.
an array of selection proportions. Rows and columns correspond to nodes in the graph. Indices along the third dimension correspond to different parameters controlling the level of sparsity in the underlying algorithm.
a matrix of signs of
Pearson's correlations estimated from xdata.
a list
with type="graphical_model" and values used for arguments
implementation, start, resampling, cpss and
PFER_method.
a list with values used for arguments
K, pi_list, tau, n_cat, pk, n
(number of observations in xdata), PFER_thr, FDP_thr,
seed, lambda_other_blocks, and Sequential_template.
The rows of S, Lambda, Q, Q_s, P,
PFER, FDP, S_2d, PFER_2d and FDP_2d, and
indices along the third dimension of selprop are ordered in the same
way and correspond to parameter values stored in Lambda. For
multi-block inference, the columns of S, Lambda, Q,
Q_s, P, PFER and FDP, and indices along the
third dimension of S_2d correspond to the different blocks.
data matrix with observations as rows and variables as columns. For multi-block stability selection, the variables in data have to be ordered by group.
optional vector encoding the grouping structure. Only used for
multi-block stability selection where pk indicates the number of
variables in each group. If pk=NULL, single-block stability
selection is performed.
matrix of parameters controlling the level of sparsity in the
underlying feature selection algorithm specified in implementation.
If implementation="glassoFast", Lambda contains penalty
parameters.
optional vector of parameters controlling the
level of sparsity in neighbour blocks for the multi-block procedure. To use
jointly a specific set of parameters for each block,
lambda_other_blocks must be set to NULL (not recommended).
Only used for multi-block stability selection, i.e. if length(pk)>1.
vector of thresholds in selection proportions. If
n_cat=NULL or n_cat=2, these values must be >0 and
<1. If n_cat=3, these values must be >0.5 and
<1.
number of resampling iterations.
subsample size. Only used if resampling="subsampling" and
cpss=FALSE.
value of the seed to initialise the random number generator and
ensure reproducibility of the results (see set.seed).
computation options for the stability score. Default is
NULL to use the score based on a z test. Other possible values are 2
or 3 to use the score based on the negative log-likelihood.
function to use for graphical modelling. If
implementation=PenalisedGraphical, the algorithm implemented in
glassoFast is used for regularised estimation of
a conditional independence graph. Alternatively, a user-defined function
can be provided.
character string indicating if the algorithm should be
initialised at the estimated (inverse) covariance with previous penalty
parameters (start="warm") or not (start="cold"). Using
start="warm" can speed-up the computations, but could lead to
convergence issues (in particular with small Lambda_cardinal). Only
used for implementation=PenalisedGraphical (see argument
"start" in glassoFast).
logical indicating if the correlation (scale=TRUE) or
covariance (scale=FALSE) matrix should be used as input of
glassoFast if
implementation=PenalisedGraphical. Otherwise, this argument must be
used in the function provided in implementation.
resampling approach. Possible values are:
"subsampling" for sampling without replacement of a proportion
tau of the observations, or "bootstrap" for sampling with
replacement generating a resampled dataset with as many observations as in
the full sample. Alternatively, this argument can be a function to use for
resampling. This function must use arguments named data and
tau and return the IDs of observations to be included in the
resampled dataset.
logical indicating if complementary pair stability selection
should be done. For this, the algorithm is applied on two non-overlapping
subsets of half of the observations. A feature is considered as selected if
it is selected for both subsamples. With this method, the data is split
K/2 times (K models are fitted). Only used if
PFER_method="MB".
method used to compute the upper-bound of the expected
number of False Positives (or Per Family Error Rate, PFER). If
PFER_method="MB", the method proposed by Meinshausen and Bühlmann
(2010) is used. If PFER_method="SS", the method proposed by Shah and
Samworth (2013) under the assumption of unimodality is used.
threshold in PFER for constrained calibration by error
control. If PFER_thr=Inf and FDP_thr=Inf, unconstrained
calibration is used (the default).
threshold in the expected proportion of falsely selected
features (or False Discovery Proportion) for constrained calibration by
error control. If PFER_thr=Inf and FDP_thr=Inf, unconstrained
calibration is used (the default).
logical indicating if the input datasets xdata and
ydata should be included in the output.
logical indicating if a loading bar and messages should be printed.
additional parameters passed to the functions provided in
implementation or resampling.