Multivariate Elastic Net Regression

Implements multivariate elastic net regression.

joinet(
  Y,
  X,
  family = "gaussian",
  nfolds = 10,
  foldid = NULL,
  type.measure = "deviance",
  alpha.base = 1,
  alpha.meta = 1,
  weight = NULL,
  sign = NULL,
  ...
)

Arguments

Y

outputs: numeric matrix with \(n\) rows (samples) and \(q\) columns (outputs)

X

inputs: numeric matrix with \(n\) rows (samples) and \(p\) columns (inputs)

family

distribution: vector of length \(1\) or \(q\) with entries "gaussian", "binomial" or "poisson"

nfolds

number of folds

foldid

fold identifiers: vector of length \(n\) with entries between \(1\) and nfolds; or NULL (balance)

type.measure

loss function: vector of length \(1\) or \(q\) with entries "deviance", "class", "mse" or "mae" (see cv.glmnet)

alpha.base

elastic net mixing parameter for base learners: numeric between \(0\) (ridge) and \(1\) (lasso)

alpha.meta

elastic net mixing parameter for meta learners: numeric between \(0\) (ridge) and \(1\) (lasso)

weight

input-output relations: matrix with \(p\) rows (inputs) and \(q\) columns (outputs) with entries \(0\) (exclude) and \(1\) (include), or NULL (see details)

sign

output-output relations: matrix with \(q\) rows ("meta-inputs") and \(q\) columns (outputs), with entries \(-1\) (negative), \(0\) (none), \(1\) (positive) and \(NA\) (any), or NULL (see details)

...

further arguments passed to glmnet

Value

This function returns an object of class joinet. Available methods include predict, coef, and weights. The slots base and meta each contain \(q\)cv.glmnet-like objects.

Details

input-output relations: In this matrix with \(p\) rows and \(q\) columns, the entry in the \(j\)th row and the \(k\)th column indicates whether the \(j\)th input may be used for modelling the \(k\)th output (where \(0\) means "exclude" and \(1\) means "include"). By default (sign=NULL), all entries are set to \(1\).

output-output relations: In this matrix with \(q\) rows and \(q\) columns, the entry in the \(l\)th row and the \(k\)th column indicates how the \(l\)th output may be used for modelling the \(k\)th output (where \(-1\) means negative effect, \(0\) means no effect, \(1\) means positive effect, and \(NA\) means any effect).

There are three short-cuts for filling up this matrix: (1) sign=1 sets all entries to \(1\) (non-negativity constraints). This is useful if all pairs of outcomes are assumed to be positively correlated (potentially after changing the sign of some outcomes). (2) code=NA sets all diagonal entries to \(1\) and all off-diagonal entries to NA (no constraints). (3) sign=NULL uses Spearman correlation to determine the entries, with \(-1\) for significant negative, \(0\) for insignificant, \(1\) for significant positive correlations.

elastic net: alpha.base controls input-output effects, alpha.meta controls output-output effects; lasso renders sparse models (alpha\(=1\)), ridge renders dense models (alpha\(=0\))

References

Armin Rauschenberger, Enrico Glaab (2021) "Predicting correlated outcomes from molecular data" Bioinformatics. btab576 doi: 10.1093/bioinformatics/btab576

See also

cv.joinet, vignette

Examples