Select features via the cluster representative lasso (Bühlmann et. al. 2013)

Select features via the cluster representative lasso (Bühlmann et. al. 2013)

Usage

clusterRepLasso(X, y, clusters = list(), nlambda = 100)

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 p >= 2 features/predictors

y

The response; A length n numeric (or integer) real-valued vector.

clusters

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). 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).

nlambda

Integer; the number of lambda values to use in the lasso fit for the cluster representative lasso. Default is 100 (following the default for glmnet). For now, nlambda must be at least 2 (using a single lambda is not supported).

Value

A list with three elements.

selected_sets

A list of integer vectors. Entry k of this list contains a selected set (an integer vector) of size k yielded by the lasso--each member of the set is the index of a single feature from a cluster selected by the cluster representative lasso (the prototype from that cluster--the cluster member most highly correlated with y). (If no set of size k was selected, entry k will be empty.)

selected_clusts_list

A list; each element of the list is a named list of selected clusters. (That is, if a selected set of size k was yielded by the cluster representative lasso, then selected_clusts_list[k] is a named list of length k, where each member of the list is an integer vector of cluster members. Note that selected_clusts_lists[k][j] will be the cluster that contains feature selected_sets[k]j.)

beta

The beta output from glmnet when the lasso was estimated on a matrix of prototypes. (See documentation for the function glmnet from the glmnet package for details.)

References

Bühlmann, P., Rütimann, P., van de Geer, S., & Zhang, C. H. (2013). Correlated variables in regression: Clustering and sparse estimation. Journal of Statistical Planning and Inference, 143(11), 1835–1858. https://doi.org/10.1016/j.jspi.2013.05.019.
Jerome Friedman, Trevor Hastie, Robert Tibshirani (2010). Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 33(1) ' 1-22. URL https://www.jstatsoft.org/v33/i01/.