SISIR {SISIR}

Interval Sparse SIR

Description

SISIR performs an automatic search of relevant intervals

Usage

SISIR(
  object,
  inter_len = rep(1, nrow(object$EDR)),
  sel_prop = 0.05,
  itermax = Inf,
  minint = 2,
  parallel = TRUE,
  ncores = NULL
)

Arguments

object

an object of class ridgeRes as obtained from the function ridgeSIR

inter_len

(numeric) vector with interval lengths for the initial state. Default is to set one interval for each variable (all intervals have length 1)

sel_prop

fraction of the coefficients that will be considered as strong zeros and strong non zeros. Default to 0.05

itermax

maximum number of iterations. Default to Inf

minint

minimum number of intervals. Default to 2

parallel

whether the computation should be performed in parallel or not. Logical. Default is FALSE

ncores

number of cores to use if parallel = TRUE. If left to NULL, all available cores minus one are used

Details

Different quality criteria used to select the best models among a list of models with different interval definitions. Quality criteria are: log-likelihood (loglik), cross-validation error as provided by the function glmnet, two versions of the AIC (AIC and AIC2) and of the BIC (BIC and BIC2) in which the number of parameters is either the number of non null intervals or the number of non null parameters with respect to the original variables

Value

S3 object of class SISIR: a list consisting of

• sEDR the estimated EDR spaces (a list of p x d matrices)

• alpha the estimated shrinkage coefficients (a list of vectors)

• intervals the interval lengths (a list of vectors)

• quality a data frame with various qualities for the model. The chosen quality measures are the same than for the function sparseSIR plus the number of intervals nbint

• init_sel_prop initial fraction of the coefficients which are considered as strong zeros or strong non zeros

• rSIR same as the input object

Author(s)

Victor Picheny, [e-mail]
Remi Servien, [e-mail]
Nathalie Vialaneix, [e-mail]

References

Picheny, V., Servien, R. and Villa-Vialaneix, N. (2016) Interpretable sparse SIR for digitized functional data. Statistics and Computing, 29(2), 255–267.

See Also

ridgeSIR, sparseSIR

Examples

set.seed(1140)
tsteps <- seq(0, 1, length = 200)
nsim <- 100
simulate_bm <- function() return(c(0, cumsum(rnorm(length(tsteps)-1, sd=1))))
x <- t(replicate(nsim, simulate_bm()))
beta <- cbind(sin(tsteps*3*pi/2), sin(tsteps*5*pi/2))
beta[((tsteps < 0.2) | (tsteps > 0.5)), 1] <- 0
beta[((tsteps < 0.6) | (tsteps > 0.75)), 2] <- 0
y <- log(abs(x %*% beta[ ,1]) + 1) + sqrt(abs(x %*% beta[ ,2]))
y <- y + rnorm(nsim, sd = 0.1)
res_ridge <- ridgeSIR(x, y, H = 10, d = 2, mu2 = 10^8)
## Not run: res_fused <- SISIR(res_ridge, rep(1, ncol(x)))