css: Cluster Stability Selection

In gregfaletto/cssr: Feature Selection Using Cluster Stability Selection

Cluster Stability Selection

Description

Executes cluster stability selection algorithm.

Usage

css(
  X,
  y,
  lambda,
  clusters = list(),
  fitfun = cssLasso,
  sampling_type = "SS",
  B = ifelse(sampling_type == "MB", 100L, 50L),
  prop_feats_remove = 0,
  train_inds = integer(),
  num_cores = 1L
)

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; can be anything that takes the form of an n-dimensional vector, with the ith entry corresponding to the ith row of X. Typically (and for default fitfun = cssLasso), y should be an n-dimensional numeric vector.
lambda	A tuning parameter or set of tuning parameters that may be used by the feature selection method fitfun. In the default case when fitfun = cssLasso, lambda should be a numeric: the penalty to use for each lasso fit. (css does not require lambda to be any particular object because for a user-specified feature selection method fitfun, lambda can be an arbitrary object. See the description of fitfun below.)
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). 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 the returned 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 provided list will be given names automatically by css. Default is list() (so no clusters are specified).
fitfun	A function; the feature selection function used on each subsample by cluster stability selection. This can be any feature selection method; the only requirement is that it accepts the arguments (and only the arguments) X, y, and lambda and returns an integer vector that is a subset of 1:p. For example, fitfun could be best subset selection or forward stepwise selection or LARS and lambda could be the desired model size; or fitfun could be the elastic net and lambda could be a length-two vector specifying lambda and alpha. Default is cssLasso, an implementation of lasso (relying on the R package glmnet), where lambda must be a positive numeric specifying the L1 penalty for the lasso.
sampling_type	A character vector; either "SS" or "MB". For "MB", all B subsamples are drawn randomly (as proposed by Meinshausen and Bühlmann 2010). For "SS", in addition to these B subsamples, the B complementary pair subsamples will be drawn as well (see Faletto and Bien 2022 or Shah and Samworth 2013 for details). Default is "SS", and "MB" is not supported yet.
B	Integer or numeric; the number of subsamples. Note: For saampling.type=="MB" the total number of subsamples will be B; for sampling_type="SS" the number of subsamples will be 2*B. Default is 100 for sampling_type="MB" and 50 for sampling_type="SS".
prop_feats_remove	Numeric; if prop_feats_remove is greater than 0, then on each subsample, each feature is randomly dropped from the design matrix that is provided to fitfun with probability prop_feats_remove (independently across features). That is, in a typical subsample, prop_feats_remove*p features will be dropped (though this number will vary). This is similar in spirit (but distinct from) extended stability selection (Beinrucker et. al. 2016); see their paper for some of the benefits of dropping features (besides increasing computational speed and decreasing memory requirements). For sampling_type="SS", the features dropped in each complementary pair of subsamples are identical in order to ensure that the theoretical guarantees of Faletto and Bien (2022) are retained within each individual pair of subsamples. (Note that this feature is not investigated either theoretically or in simulations by Faletto and Bien 2022). Must be between 0 and 1. Default is 0.
train_inds	Optional; an integer or numeric vector containing the indices of observations in X and y to set aside for model training by the function getCssPreds after feature selection. If train_inds is not provided, all of the observations in the provided data set will be used for feature selection.
num_cores	Optional; an integer. If using parallel processing, the number of cores to use for parallel processing (num_cores will be supplied internally as the mc.cores argument of parallel::mclapply).

Value

A list containing the following items:

feat_sel_mat	A B (or 2*B for sampling.method "SS") x p numeric (binary) matrix. feat_sel_mat[i, j] = 1 if feature j was selected by the base feature selection method on subsample i, and 0 otherwise.
clus_sel_mat	A B (or 2*B for SS sampling) x length(clusters) numeric (binary) matrix. clus_sel_mat[i, j] = 1 if at least one feature from cluster j was selected by the base feature selection method on subsample i, and 0 otherwise.
X	The X matrix provided to css.
y	The y vector provided to css.
clusters	A named list of integer vectors containing all of the clusters provided to css, as well as size 1 clusters of any features not listed in any of the clusters provided to css. All clusters will have names; any clusters not provided with a name in the input to css will be given names automatically by css (of the form c1, etc.).'
train_inds	Identical to the train_inds provided to css.

Author(s)

Gregory Faletto, Jacob Bien

References

Faletto, G., & Bien, J. (2022). Cluster Stability Selection. arXiv preprint arXiv:2201.00494. https://arxiv.org/abs/2201.00494.
Shah, R. D., & Samworth, R. J. (2013). Variable selection with error control: Another look at stability selection. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 75(1), 55–80. https://doi.org/10.1109/RITA.2014.2302071.
Meinshausen, N., & Bühlmann, P. (2010). Stability Selection. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 72(4), 417–473. https://rss.onlinelibrary.wiley.com/doi/full/10.1111/j.1467-9868.2010.00740.x.
Beinrucker, A., Dogan, Ü., & Blanchard, G. (2016). Extensions of stability selection using subsamples of observations and covariates. Statistics and Computing, 26(5), 1059- 1077. https://doi.org/10.1007/s11222-015-9589-y.

gregfaletto/cssr documentation built on March 3, 2023, 1 p.m.