conformal.multidim.jackplus {conformalInference.multi}

Multivariate Response Jackknife + Prediction Regions

Description

Compute prediction regions using multivariate Jackknife + inference.

Usage

conformal.multidim.jackplus(x, y, x0, train.fun, predict.fun, alpha = 0.1)

Arguments

x

The feature variables, a matrix n x p.

y

The matrix of multivariate responses (dimension n x q)

x0

The new points to evaluate, a matrix of dimension n0 x p.

train.fun

A function to perform model training, i.e., to produce an estimator of E(Y|X), the conditional expectation of the response variable Y given features X. Its input arguments should be x: matrix of features, and y: matrix of responses.

predict.fun

A function to perform prediction for the (mean of the) responses at new feature values. Its input arguments should be out: output produced by train.fun, and newx: feature values at which we want to make predictions.

alpha

Miscoverage level for the prediction intervals, i.e., intervals with coverage 1-alpha are formed. Default for alpha is 0.1.

Details

The work is an extension of the univariate approach to jackknife + inference to a multivariate context, exploiting the concept of depth measures.

This function is based on the package future.apply to perform parallelisation. If this package is not installed, then the function will abort.

Value

A list with length n0, giving the lower and upper bounds for each observation.

Examples

## One instance

n=50
p=3
q=2
mu=rep(0,p)
x = mvtnorm::rmvnorm(n, mu)
beta<-sapply(1:q, function(k) c(mvtnorm::rmvnorm(1,mu)))
y = x%*%beta + t(mvtnorm::rmvnorm(q,1:n))
x0=matrix(x[n,],nrow=1)
y0=matrix(y[n,],nrow=1)
n0<-nrow(y0)
funs=lm_multi()

sol<-conformal.multidim.jackplus(x,y,x,train.fun = funs$train.fun,
                                      predict.fun = funs$predict.fun,alpha=0.05)

sol