Infer the model-free variable importance, mMSE gap via floodgate

This function infers the model-free variable importance, mMSE gap via floodgate.

floodgate(
  X,
  Y,
  i1,
  i2,
  nulls.list = NULL,
  gamma_X.list = NULL,
  sigma_X.list = NULL,
  Xmodel = "gaussian",
  funs,
  algo = "lasso",
  cv.rule = "min",
  one.sided = TRUE,
  alevel = 0.05,
  test = "z",
  verbose = TRUE
)

Arguments

X

a n by p matrix, containing all the covariates.
Y

a n by 1 matrix, containing the response variables.
i1

the index of training samples.
i2

the index of inference samples.
nulls.list

a list of length p, whose element is a (|i2|*K)-dimensional vector, which contains K set of null samples.
gamma_X.list

a list of length p, with each element being the linear coefficient of the given covariate on the other covariates (only relevant when Xmodel = "gaussian"; default: NULL).
sigma_X.list

a list of length p, with each element being the variance of the conditional distribution.
Xmodel

model of the covaraites (default: "gaussian").
funs

a list of three: train.fun, active.fun and predict.fun.
algo

a fitting algorithm (default: "lasso").
cv.rule

indicates which rule should be used for the predict function, either "min" (the usual rule) or "1se" (the one-standard- error rule); default: "min"). See the glmnet help files for details.
one.sided

whether to obtain LCB or p-values via the one-sided way (default: TRUE).
alevel

confidence level (defaul: 0.05).
test

type of the hypothesis test (defaul: "z").
verbose

whether to show intermediate progress (default: FALSE).

Value

A list of three objects. inf.out: a matrix of |S|-by-4, containing the p-values, LCI, UCI and the floodgate LCB for variable in S; S: a list of selected variables; cpu.time: computing time.

References

Zhang L, Janson L (2020). “Floodgate: Inference for Model-Free Variable Importance.” arXiv preprint arXiv:2007.01283.

See also

Other methods: calculate.V_mean(), calulate.mu_Xk(), fg.inference.binary(), fg.inference(), fit.mu(), floodgate.binary(), inference_general()