conformal.multidim.msplit: Multi Split conformal prediction intervals with Multivariate...

In paolo-vergo/conformalInference.multi: Conformal Inference Tools for Regression with Multivariate Response

Multi Split conformal prediction intervals with Multivariate Response

Description

Compute prediction intervals using Multi Split conformal inference with multivariate response.

Usage

conformal.multidim.msplit(
  x,
  y,
  x0,
  train.fun,
  predict.fun,
  alpha = 0.1,
  split = NULL,
  seed = FALSE,
  randomized = FALSE,
  seed_beta = FALSE,
  verbose = FALSE,
  training_size = NULL,
  score = "max",
  s_type = "st-dev",
  B = 100,
  lambda = 0,
  tau = 1 - (B + 1)/(2 * B)
)

Arguments

x	The feature variables, a matrix nxp.
y	The matrix of multivariate responses (dimension nxq)
x0	The new points to evaluate, a matrix of dimension n0xp.
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.
split	Indices that define the data-split to be used (i.e., the indices define the first half of the data-split, on which the model is trained). Default is NULL, in which case the split is chosen randomly.
seed	Integer to be passed to set.seed before defining the random data-split to be used. Default is FALSE, which effectively sets no seed. If both split and seed are passed, the former takes priority and the latter is ignored.
randomized	Should the randomized approach be used? Default is FALSE.
seed_beta	The seed for the randomized version. Default is FALSE.
verbose	Should intermediate progress be printed out? Default is FALSE.
training_size	Split proportion between training and calibration set. Default is 0.5.
score	The chosen score for the split conformal function.
s_type	The type of modulation function. Currently we have 3 options: "identity","st-dev","alpha-max". Default is "std-dev"
B	Number of repetitions. Default is 100.
lambda	Smoothing parameter. Default is 0.
tau	It is a smoothing parameter: tau=1-1/B Bonferroni intersection method tau=0 unadjusted intersection Default is 1-(B+1)/(2*B).

Details

The work is an extension of the univariate approach to Multi Split conformal inference to a multivariate context.

This function is based on the package future.apply to perform parallelization.

Value

A list with the following components x0, lo, up. In particular lo and up are matrices of dimension n0 x q.

References

"Multi Split Conformal Prediction" by Solari, Djordjilovic (2021) is the baseline for the univariate case.

Examples

n = 33
n0 = 2
p = 2
mu = rep(0,p)
x = mvtnorm::rmvnorm(n, mu)
my_grid <- seq(from=0,to=1,length.out=2)
y = t(apply(x,1,function(u) u[1] + u[2]*cos(6*pi*my_grid)))
x0 = mvtnorm::rmvnorm(n0, mu)
fun=mean_multi()
#fun=lm_multi()

B=3

final.multi=conformal.multidim.msplit(x=x,y=y, x0=x0,
                                      fun$train.fun, fun$predict.fun,
                       alpha=0.1,
                       split=NULL, seed=FALSE, randomized=FALSE,seed_beta=FALSE,
                       verbose=FALSE, training_size=NULL,s_type="st-dev",B=B,lambda=0,
                       score="l2")

paolo-vergo/conformalInference.multi documentation built on July 4, 2023, 9:50 a.m.