| Type: | Package |
| Title: | Beyond Pareto: Bi-Objective and Multi-Objective Regression Trees’ |
| Version: | 0.1.0 |
| Author: | Erick G.G. de Paz 
[aut, cre],
Arturo Hernández-Aguirre
[aut],
Iván Cruz-Aceves
[aut] |
| Maintainer: | Erick G.G. de Paz <erick.giles@cimat.mx> |
| Description: | Implements the Bi-objective Regression Tree (BORT) for efficiently learning vector-valued functions. Unlike traditional methods that rely on constructing multiple models or static scalarisation, BORT integrates the exploration of the Pareto front directly into a single tree's growth process. It provides high-efficiency, single-model approaches that can Pareto-dominate entire Pareto-consistent families of trees, supported by a C backend for fast computation. For more details see Paz (2026) <doi:10.1007/978-3-032-28393-1_2> and Paz (2025) <doi:10.1007/978-3-031-78401-9_2>. |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| NeedsCompilation: | yes |
| Repository: | CRAN |
| Date: | 2026-07-01 |
| Depends: | R (≥ 2.10.0) |
| Packaged: | 2026-07-01 23:27:53 UTC; erick |
| Date/Publication: | 2026-07-07 09:50:08 UTC |
BORT: Multi-objective Regression Trees
Description
Constructs a multiobjective regression tree or a Pareto-consistent family of trees based on a top-down generalisation. The partitioning process selects the hyper-rectangle with the maximum Lebesgue measure. The split thresholds are chosen to minimise the sum of the Weighted Mean Squared Error across dimensions.
Usage
bort(X, Y, k = 1, type = c("PARETO", "BORT"), minSample = NULL)
Arguments
X |
A numeric matrix of size |
Y |
A numeric matrix of size |
k |
An integer scalar specifying the number of trees to generate. Default is 1. |
type |
A character string indicating the modelling strategy. |
minSample |
An integer indicating the minimum number of samples a node must contain to be eligible for further splitting. If |
Details
This implementation maps continuous multiobjective functions f:\mathbb{R}^{p}\rightarrow\mathbb{R}^{q}. It partitions the Cartesian space D bounded by [min(X[,i]) - \delta, max(X[,i]) + \delta], where \delta= 0.1*(max(X[,i])-min(X[,i])).
For type = "PARETO", scalarisation of errors uses a constant weight vector across the tree depth. For type = "BORT", a novel weighting approach selects random weights at every partition, achieving efficient single-model dominance over entirely consistent families. Both approaches are explained in de Paz (2025).
Value
A list of length k containing R functions. Each function accepts a numeric vector x of length p and returns a predicted numeric vector y of length q.
References
de Paz, E.G.G., Hernández-Aguirre, A., Cruz-Aceves, I. (2026). Beyond Pareto: A High-Efficiency Approach to Bi-objective Regression Trees. In Pattern Recognition. Springer Nature Switzerland. doi:10.1007/978-3-032-28393-1_2
de Paz, E.G.G., Vaquera Huerta, H., Albores Velasco, F.J., Bauer Mengelberg, J.R., Romero Padilla, J.M. (2025). A Splitting Criterion for CART Models Based on Bayesian Optimisation. In Statistics, Society and Environment. Springer Nature Switzerland. doi:10.1007/978-3-031-78401-9_2
Examples
# Ensure the C shared library is loaded before running
# dyn.load(paste0("multiobjective_tree", .Platform$dynlib.ext))
# Prepare the iris dataset
data(iris)
X <- as.matrix(iris[, 1:2]) # Sepal.Length, Sepal.Width
Y <- as.matrix(iris[, 3:4]) # Petal.Length, Petal.Width
# Generate a single BORT model
bort_models <- bort(X, Y, k = 1, type = "BORT")
# Predict for the first instance
test_point <- X[1, ]
prediction <- bort_models[[1]](test_point)
print(prediction)
# Generate a Pareto-consistent family of 5 trees
pareto_models <- bort(X, Y, k = 5, type = "PARETO")
pred_pareto <- pareto_models[[1]](test_point)
print(pred_pareto)