conformal.fun.msplit: Functional Multi Split conformal prediction intervals.

In paolo-vergo/conformalInference.fd: Tools for Conformal Inference for Regression in Multivariate Functional Setting

Functional Multi Split conformal prediction intervals.

Description

Compute prediction intervals using functional multi split conformal inference.

Usage

conformal.fun.msplit(
  x,
  t,
  y_val,
  x0,
  train.fun,
  predict.fun,
  alpha = 0.1,
  split = NULL,
  seed = FALSE,
  randomized = FALSE,
  seed_beta = FALSE,
  verbose = FALSE,
  training_size = NULL,
  s_type,
  B = 100,
  lambda = 0,
  tau = 1 - (B + 1)/(2 * B)
)

Arguments

x	The input variable, a list of n elements. Each element is composed by a list of p vectors(with variable length, since the evaluation grid may change).
t	The grid points for the evaluation of function y_val. It has the same structure as x (list of list of vector).
y_val	The response variable. It is either, as with x and t, a list of list of vectors or an fda object (of type fd, fData, mfData).
x0	The new points to evaluate, a list of n0 elements. Each element is composed by a list of p vectors(with variable length).
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: list of features, and y: list 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 of the conformal.split.fun. Default is FALSE.
verbose	Should intermediate progress be printed out? Default is FALSE.
training_size	Vector containing the split proportion between training and calibration set. It has B components. Default is 0.5.
s_type	The type of modulation function. Currently we have 3 options: "identity","st-dev","alpha-max".
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 functional context.

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

Value

A list of the following: lo,up,grid_size,tn.

References

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

Examples

## fData #############################

N = 30
P = 60
grid = seq( 0, 1, length.out = P )
C = roahd::exp_cov_function( grid, alpha = 0.3, beta = 0.4 )
values = roahd::generate_gauss_fdata( N,
                                      centerline = sin( 2 * pi * grid ),
                                      Cov = C )
fD = roahd::fData( grid, values )
x0=list(as.list(grid))
fun=mean_lists()
B=4

final.multi=conformal.fun.msplit(NULL,NULL, fD, 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,lambda=0,
                                 tau = 0)

###  mfData ###################################

N = 50
P = 50
t0 = 0
t1 = 1
grid = seq( t0, t1, length.out = P )
C = roahd::exp_cov_function( grid, alpha = 0.3, beta = 0.4 )
Data_1 = roahd::generate_gauss_fdata( N, centerline = sin( 2 * pi * grid ), Cov = C )
Data_2 = roahd::generate_gauss_fdata( N, centerline = log(1+ 2 * pi * grid ), Cov = C )
mfD=roahd::mfData( grid, list( Data_1, Data_2 ) )
x0=list(as.list(grid))
fun=mean_lists()
B=4
final.multi=conformal.fun.msplit(NULL,NULL, mfD, 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,lambda=0,
                                 tau = 1-(B+1)/(2*B))


### fd ###########################################
daybasis <- fda::create.fourier.basis(c(0, 365), nbasis=25)
tempfd <- fda::smooth.basis(fda::day.5, fda::CanadianWeather$dailyAv[,,"Temperature.C"],daybasis)$fd
Lbasis <- fda::create.constant.basis(c(0, 365))
Lcoef <- matrix(c(0,(2*pi/365)^2,0),1,3)
bfdobj <- fda::fd(Lcoef,Lbasis)
bwtlist <- fda::fd2list(bfdobj)
harmaccelLfd <- fda::Lfd(3, bwtlist)
Ltempmat <- fda::eval.fd(fda::day.5, tempfd, harmaccelLfd)
t=1:365
x0=list(as.list(grid))
fun=mean_lists()
B=4
final.multi=conformal.fun.msplit(NULL,fda::day.5, tempfd, 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,lambda=0,
                        tau = 0.2)

paolo-vergo/conformalInference.fd documentation built on Oct. 14, 2023, 12:47 a.m.