sfpl_approx {SFPL}

Approximate Sparse Fused Plackett-Luce

Description

Contains an approximate (typically faster) version of the main function of this package that is used to estimate the parameter of interest \beta. We recommend this version due to its (relatively) fast convergence.

Usage

sfpl_approx(x, y, ls_vec, lf_vec, epsilon, verbose)

Arguments

x

A M \times p matrix containing the values for the p objects variables across the M objects.

y

A list consisting of K matrices with each matrix containing (partial) rankings across n observations for group k.

ls_vec

Vector containing shrinkage parameters.

lf_vec

Vector containing fusion penalty parameters.

epsilon

Small positive value used to ensure that the penalty function is differentiable. Typically set at 10^{-5}.

verbose

Boolean that returns the process of the parameter estimation.

Value

beta_est

A list of length ls_vec\timeslf_vec that contains the parameter estimates \hat{beta} for each combination of ls_vec and lf_vec.

Author(s)

Sjoerd Hermes
Maintainer: Sjoerd Hermes [e-mail]

References

1. Hermes, S., van Heerwaarden, J., and Behrouzi, P. (2024). Joint Learning from Heterogeneous Rank Data. arXiv preprint, arXiv:2407.10846

Examples

# we first obtain the rankings and object variables
data(ghana)
y <- list(ghana[[1]], ghana[[2]])
x <- ghana[[3]]

# our next step consists of creating two vectors for the penalty parameters
ls_vec <- lf_vec <- c(0, 0.25)

# we choose epsilon to be small: 10^(-5), as we did in Hermes et al., (2024)
# now we can fit our model
epsilon <- 10^(-5)
verbose <- FALSE

result <- sfpl_approx(x, y, ls_vec, lf_vec, epsilon, verbose)