Obtain a selected set of clusters and features using cluster stability selection

Takes in data X and y and returns a set of clusters (and a set of features) that are useful for predicting y from the data in X. This is a wrapper function for css and getCssSelections. Using cssSelect is simpler, but it has fewer options, and it executes the full (computationally expensive) subsampling procedured every time it is called. In contrast, css can be called just once, and then getCssSelections can quickly return results using different values of cutoff, max_num_clusts, etc. from the calculations done in one call to css.

Usage

cssSelect(
  X,
  y,
  clusters = list(),
  lambda = NA,
  cutoff = NA,
  max_num_clusts = NA,
  auto_select_size = TRUE,
  alpha = 1
)

Arguments

X: An n x p numeric matrix (preferably) or a data.frame (which will be coerced internally to a matrix by the function model.matrix) containing the p >= 2 features/predictors. Must not contain missing (NA) values.
y: A length-n numeric vector containing the responses; y[i] is the response corresponding to observation X[i, ]. (Note that for the css function, y does not have to be a numeric response, but for this function, the underlying selection procedure is the lasso, so y must be a real-valued response.)
clusters: Optional; either an integer vector of a list of integer vectors; each vector should contain the indices of a cluster of features (a subset of 1:p). (If there is only one cluster, clusters can either be a list of length 1 or an integer vector.) All of the provided clusters must be non-overlapping. Every feature not appearing in any cluster will be assumed to be unclustered (that is, they will be treated as if they are in a "cluster" containing only themselves). If clusters is a list of length 0 (or a list only containing clusters of length 1), then css() returns the same results as stability selection (so feat_sel_mat will be identical to clus_sel_mat). Names for the clusters will be needed later; any clusters that are not given names in the list clusters will be given names automatically by css. CAUTION: if the provided X is a data.frame that contains a categorical feature with more than two levels, then the resulting matrix made from model.matrix will have a different number of columns than the provided data.frame, some of the feature numbers will change, and the clusters argument will not work properly (in the current version of the package). To get correct results in this case, please use model.matrix to convert the data.frame to a numeric matrix on your own, then provide this matrix and cluster assignments with respect to this matrix. Default is list() (so no clusters are specified, and every feature is assumed to be in a "cluster" containing only itself).
lambda: Optional; the tuning parameter to be used by the lasso for feature selection in each subsample. If lambda is not provided, cssSelect will choose one automatically by cross-validation. Default is NA.
cutoff: Numeric; cssSelect will only select those clusters with selection proportions equal to at least cutoff. Must be between 0 and 1. Default is NA (in which case max_num_clusts are used).
max_num_clusts: Integer or numeric; the maximum number of clusters to use regardless of cutoff. (That is, if the chosen cutoff returns more than max_num_clusts clusters, the cutoff will be decreased until at most max_num_clusts clusters are selected.) Default is NA (in which case either cutoff is used to choose the number of clusters, or if cutoff was also unspecified, cssSelect chooses max_num_clusts by cross-validation).
auto_select_size: Logical; if TRUE, then max_num_clusts will be automatically estimated using the lasso with cross-validation. Default is TRUE, though this argument is ignored if either cutoff or max_num_clusts is provided. (If desired output is to return all clusters, you should set auto_select_size to FALSE and do not provide cutoff or max_num_clusts.)
alpha: Numeric; the elastic net mixing parameter. Must be in (0, 1]. Drives both the choice of lambda (when lambda is not provided) and the elastic net fit used for feature selection in each subsample. Default is 1 (in which case the penalty is the lasso).

Value

A named list with three items.

selected_clusts: A named list of integer vectors; each vector contains the indices of the features in one of the selected clusters.
selected_feats: A named integer vector; the indices of the features with nonzero weights from all of the selected clusters.
weights: A named list of the same length as selected_clusts. Each list element weights[[j]] is a numeric vector of the weights to use for the jth selected cluster, and it has the same name as the cluster it corresponds to.

Author

Gregory Faletto, Jacob Bien

Examples

set.seed(1)
data <- genClusteredData(n = 80, p = 11, k_unclustered = 2,
  cluster_size = 4, n_clusters = 1, snr = 3)
clusters <- list(cluster1 = 1:4)
res <- cssSelect(X = data$X, y = data$y, clusters = clusters)
res$selected_feats
#> [1] 2 5 6