Percentage-Error Support Vector Regression

Implements four support vector regression (SVR) models derived from a unified mathematical framework for percentage-error loss functions: epsilon-SVR minimizing the mean absolute percentage error (MAPE), its symmetric kernel extension, least-squares SVR (LS-SVR) minimizing the root mean square percentage error (RMSPE), and its symmetric counterpart. All models require strictly positive targets. The epsilon-SVR models are solved via a built-in sequential minimal optimization (SMO) algorithm (with 'osqp' available as an optional alternative backend) and the LS-SVR models via a linear system (base R). See Benavides-Herrera et al. (2026) for the mathematical derivations.

psvr

psvr implements four support vector regression models derived from a unified mathematical framework for percentage-error loss functions. Classical SVR minimises absolute-error losses (MAE, MSE), which are scale-dependent: an error of 1 unit is negligible when the target is 1 000 but critical when it is 2. psvr addresses this by optimising MAPE and RMSPE directly, making it well-suited for forecasting tasks where targets are strictly positive and relative accuracy is what matters.

There is one fitter per model family, and sym_type selects the symmetric variant within each:

sym_type = "even" imposes an even-function prior (f(-x) = f(x)), "odd" an odd one. All models require strictly positive targets (y > 0).

Installation

# CRAN
install.packages("psvr")

# Development version from GitHub
pak::pak("pbenavidesh/psvr")

Quick start

library(psvr)

# Synthetic dataset: even function (f(-x) = f(x)), targets strictly positive
set.seed(42)
n  <- 100
X  <- matrix(rnorm(n * 2), n, 2)
y  <- 2 + X[, 1]^2 + 0.5 * X[, 2]^2 + rnorm(n, sd = 0.1)

tr <- 1:70;  te <- 71:100
X_tr <- X[tr, ];  y_tr <- y[tr]
X_te <- X[te, ];  y_te <- y[te]

# Standardise features using training-set statistics (important for RBF)
col_mean <- colMeans(X_tr);  col_sd <- apply(X_tr, 2, sd)
X_tr_s   <- scale(X_tr, col_mean, col_sd)
X_te_s   <- scale(X_te, col_mean, col_sd)

K <- make_kernel("rbf", sigma = 1)

# Model 1 — ε-SVR with MAPE
fit1  <- psvr_mape(X_tr_s, y_tr, kernel = K, C = 0.5, eps = 5)
pred1 <- predict(fit1, X_te_s)

# Model 2 — Symmetric ε-SVR with MAPE  (even-function prior)
fit2  <- psvr_mape(X_tr_s, y_tr, sym_type = "even", kernel = K, C = 0.5, eps = 5)
pred2 <- predict(fit2, X_te_s)

# Model 3 — LS-SVR with RMSPE
fit3  <- psvr_rmspe(X_tr_s, y_tr, kernel = K, gamma = 100)
pred3 <- predict(fit3, X_te_s)

# Model 4 — Symmetric LS-SVR with RMSPE  (even-function prior)
fit4  <- psvr_rmspe(X_tr_s, y_tr, sym_type = "even", kernel = K, gamma = 100)
pred4 <- predict(fit4, X_te_s)

mape <- function(y, yhat) mean(abs(y - yhat) / y) * 100

cat(sprintf("Model 1 (MAPE e-SVR):       MAPE = %.2f%%", mape(y_te, pred1)),
    sprintf("Model 2 (MAPE sym e-SVR):   MAPE = %.2f%%", mape(y_te, pred2)),
    sprintf("Model 3 (RMSPE LS-SVR):     MAPE = %.2f%%", mape(y_te, pred3)),
    sprintf("Model 4 (RMSPE sym LS-SVR): MAPE = %.2f%%", mape(y_te, pred4)),
    sep = "\n")
#> Model 1 (MAPE e-SVR):       MAPE = 3.57%
#> Model 2 (MAPE sym e-SVR):   MAPE = 5.97%
#> Model 3 (RMSPE LS-SVR):     MAPE = 3.76%
#> Model 4 (RMSPE sym LS-SVR): MAPE = 5.79%

For a full worked example on ggplot2::mpg — including a 70/30 train–test split, feature standardisation, and comparison against a linear baseline — see vignette("getting-started", package = "psvr").

Reference

Benavides-Herrera, P., Álvarez, G., Ruiz-Cruz, R., & Sánchez-Torres, J. D. (2026). A unified family of percentage-error support vector regression models with symmetric kernel extensions. Mathematics, 14(10), 1679. https://doi.org/10.3390/math14101679