Estimates a ranking of edges for a given query, e.g. for parental relations in the underlying causal graph structure, using various possible methods.
Supported methods at the moment are ARGES, backShift, bivariateANM, bivariateCAM, CAM, FCI, FCI+, GES, GIES, hiddenICP, ICP, LINGAM, MMHC, rankARGES, rankFci, rankGES, rankGIES, rankPC, regression, RFCI and PC.
getRanking(
X,
environment,
interventions = NULL,
queries = c("isParent", "isMaybeParent", "isNoParent", "isAncestor",
"isMaybeAncestor", "isNoAncestor"),
method = c("ICP", "hiddenICP", "backShift", "pc", "LINGAM", "ges", "gies", "CAM",
"fci", "rfci", "regression", "bivariateANM", "bivariateCAM")[1],
alpha = 0.1,
variableSelMat = NULL,
excludeTargetInterventions = TRUE,
onlyObservationalData = FALSE,
indexObservationalData = NULL,
setOptions = list(),
assumeNoSelectionVars = TRUE,
nsim = 100,
sampleSettings = 1/sqrt(2),
sampleObservations = 1/sqrt(2),
verbose = FALSE,
...
)A \((n x p)\)-data matrix with \(n\) observations of \(p\) variables.
A vector of length \(n\), where the entry for
observation \(i\) is an index for the environment in which observation \(i\) took
place (simplest case entries 1 for observational data and entries
2 for interventional data of unspecified type). Is required for
methods ICP, hiddenICP, backShift.
A optional list of length n. The entry for observation
i is a numeric vector that specifies the variables on which interventions
happened for observation i (a scalar if an intervention happened on just
one variable and numeric(0) if no intervention occured for this
observation). Is used for method gies but will generate the vector
environment if this is set to NULL (even though it might
generate too many different environments for some data so a hand-picked
vector environment is preferable). Is also used for ICP and
hiddenICP to exclude interventions on the target variable of
interest.
One (or more of) "isParent", "isMaybeParent", "isNoParent", "isAncestor","isMaybeAncestor", "isNoAncestor"
A string that specfies the method to use. The methods
pc (PC-algorithm), LINGAM (LINGAM), arges (Adaptively
restricted greedy equivalence search), ges
(Greedy equivalence search), gies (Greedy interventional equivalence
search), fci (Fast causal inference)
and rfci (Really fast causal inference) are imported from the
package "pcalg" and are documented there in more detail, including the
additional options that can be supplied via setOptions. The method
CAM (Causal additive models) is documented in the package "CAM" and
the methods ICP (Invariant causal prediction), hiddenICP
(Invariant causal prediction with hidden variables) are from the package
"InvariantCausalPrediction". The method backShift comes from the
package "backShift". The method mmhc comes from the
package "bnlearn".
Finally, the methods bivariateANM and
bivariateCAM are for now implemented internally but will hopefully
be part of another package at some point in the near future.
The level at which tests are done. This leads to confidence
intervals for ICP and hiddenICP and is used internally for
pc and rfci.
An optional logical matrix of dimension (pxp). An
entry TRUE for entry (i,j) says that variable i should be considered
as a potential parent for variable j and vice versa for FALSE. If the
default value of NULL is used, all variables will be considered, but
this can be very slow, especially for methods pc, ges,
gies, rfci and CAM.
When looking for parents of variable k
in 1,...,p, set to TRUE if observations where an intervention on
variable k occured should be excluded. Default is TRUE.
If set to TRUE, only observational data
is used. It will take the index in environment specified by
indexObservationalData. If environment is NULL, all
observations are used. Default is FALSE.
Index in environment that encodes
observational data. Default is 1.
A list that can take method-specific options; see the individual documentations of the methods for more options and their possible values.
Set to TRUE is you want to assume the absence
of selection variables.
The number of resamples for stability selection.
The fraction of different environments to resample in each resampling (at least two different environments will be selected so the argument is without effect if there are just two different environments in total).
The fraction of samples to resample in each environment.
If TRUE, detailed output is provided.
Parameters to be passed to underlying method's function.
A list with the following entries:
ranking A list of length length(queries). For each query,
the corresponding list entry contains a matrix of dimension \((p x p) x 2\)
with the ranking of edges. E.g. the first row indicates that the edge from
ranking$isParent[1,1] to ranking$isParent[1,2] is the most likely edge according
to the method under consideration.
resList A list of length length(queries). For each query,
the corresponding list entry contains a matrix of dimension \((p x p)\) with the counts for
\(A_{i,j} = 1\) across the nsim subsamples.
simEstimates A list of length nsim with the method's
output for each of the nsim subsamples.
For both parental and ancestral relations, three queries are supported.
The existence of a relation is assessed by the queries isParent and
isAncestor; the absence of a relation is assessed by the queries
isNoParent and isNoAncestor; the potential existence of a
relation is addressed by the queries isMaybeParent and
isMaybeAncestor.
All queries return a connectivity matrix which we denote by \(A\). The interpretation of the entries of \(A\) differs according to the considered query:
Parental relations: Queries concerning parental relations can only be answered by those methods under consideration that return a DAG, a CPDAG or a directed cyclic graph. When we say that a particular method cannot answer a given query, then the method's output with respect to this query will be the zero matrix. However, the eventual ranking for such a query will not necessarily be random due to the tie breaking scheme that is applied when ranking pairs of variables (see below).
isParent In the connectivity matrix \(A\) returned by this
query, the entry \(A_{i,j} = 1\) means that there is a directed edge
from node \(i\) to node \(j\) in the graph structure estimated by the
method under consideration. Otherwise, \(A_{i,j} = 0\).
isMaybeParent \(A_{i,j} = 1\) means that there is
a directed or an undirected edge from node \(i\) to node \(j\)
in the estimated graph structure. Otherwise, \(A_{i,j} = 0\).
isNoParent \(A_{i,j} = 1\) means that there is neither a
directed nor an undirected edge from node \(i\) to node \(j\) in the
estimated graph structure. Otherwise, \(A_{i,j} = 0\).
Ancestral relations: Queries concerning ancestral relations can be answered by all methods under consideration.
isAncestor \(A_{i,j} = 1\) means that there is a
directed path from node \(i\) to node \(j\) in the estimated graph
structure. Otherwise, \(A_{i,j} = 0\). In case of PAGs, directed paths can
contain the edge types \(i --> j\) and \(i --o j\). Including the latter
edge type in this category implies that we exclude the existence of selection
variables.
isMaybeAncestor \(A_{i,j} = 1\) then means that there is a
path from node \(i\) to node \(j\) that contains directed and/or undirected
edges. Otherwise, \(A_{i,j} = 0\). For PAGs, such paths can contain the edge
types \(i --> j\), \(i --o j\), \(i o-o j\) and/or
\(i o-> j\). Otherwise, \(A_{i,j} = 0\).
isNoAncestor \(A_{i,j} = 1\) means that there is neither a
directed path nor a partially directed path from node \(i\) to node \(j\)
in the estimated graph structure. Otherwise, \(A_{i,j} = 0\).
Stability ranking: To obtain a ranking of edges for a given set of
queries, we run the method under consideration on nsims random
subsamples of the data. In each round, we draw samples from a fraction of
settings, where the size of the fraction is specified by sampleSettings.
In each chosen setting, we sample a fraction of observations
uniformly at random without replacement, where the size of the fraction is
specified by sampleObservations.
For each subsample we randomly permute the order of the variables in the input. Methods that are order-dependent can therefore not exploit any potential advantage stemming from a data matrix with columns ordered according to the causal ordering or a similar one. We then run the method on each subsample.
For each subsample and a particular query, we obtain the corresponding
connectivity matrix \(A\). We can then rank all pairs of nodes \(i,j\)
according to the frequency of the occurrence of \(A_{i,j} = 1\) across
subsamples. Ties between pairs of variables can be broken with the results
of the other queries if they are also computed as specified by queries;
otherwise ties are broken at random:
If the query is isParent, ties are broken with counts for
isMaybeParent.
For the query isMaybeParent ties are broken with counts for
isParent, i.e. in case of equal counts we give a preference to the
edge that was considered more often to be a 'certain' parent. For methods
returning DAGs this scheme makes the ranking for isMaybeParent equal
to the result for isParent, up to the random tie breaking that is
applied for isParent.
If the query is isNoParent, ties are broken according to which
edge was selected less often in the query isMaybeParent.
If the query is isAncestor, ties are broken with counts for
isMaybeAncestor.
For the query isMaybeAncestor ties are broken with counts
for isAncestor, i.e. in case of equal counts we give a preference
to the edge that was considered more often to be a 'certain' ancestor.
For methods returning DAGs this scheme makes the ranking for isMaybeAncestor
equal to the result for isAncestor, up to the random tie breaking
that is applied for isAncestor.
If the query is isNoAncestor, ties are broken according to
which one was selected less often in the query isMaybeAncestor.
If the tie breaking matrix defined according to these rules is 0, a matrix with standard normal random entries is used to break ties. Similarly, if there are remaining ties after applying the tie breaking rules described above, ties are broken randomly.
getParents for the underlying point-estimate of
the causal graph.
# NOT RUN {
data("simDataInv")
X <- simDataInv$X
set.seed(1)
if(require(pcalg)){
rank <- getRanking(X,
environment = simDataInv$environment,
queries = c("isParent","isMaybeParent"),
method = c("LINGAM"),
verbose = FALSE)
# estimated ranking
print(rank$ranking$isParent)
# true adjacency matrix
print(simDataInv$configs$trueA)
}else{
cat("\nThe packages 'pcalg' is needed for the example to
work. Please install it.")
}
# }
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