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.
| Function | Loss | Solver |
|---|---|---|
mape_svr() |
MAPE — ε-insensitive | quadratic program (osqp) |
mape_sym_svr() |
MAPE — symmetric kernel | quadratic program (osqp) |
rmspe_lssvr() |
RMSPE — least-squares | linear system |
rmspe_sym_lssvr() |
RMSPE — symmetric kernel | linear system |
All models require strictly positive targets (y > 0).
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 <- mape_svr(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 (a = 1: even-function prior)
fit2 <- mape_sym_svr(X_tr_s, y_tr, kernel = K, C = 0.5, eps = 5, a = 1)
pred2 <- predict(fit2, X_te_s)
# Model 3 — LS-SVR with RMSPE
fit3 <- rmspe_lssvr(X_tr_s, y_tr, kernel = K, gamma = 100)
pred3 <- predict(fit3, X_te_s)
# Model 4 — Symmetric LS-SVR with RMSPE (a = 1: even-function prior)
fit4 <- rmspe_sym_lssvr(X_tr_s, y_tr, kernel = K, gamma = 100, a = 1)
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%%\n", mape(y_te, pred1)))
cat(sprintf("Model 2 (MAPE sym e-SVR): MAPE = %.2f%%\n", mape(y_te, pred2)))
cat(sprintf("Model 3 (RMSPE LS-SVR): MAPE = %.2f%%\n", mape(y_te, pred3)))
cat(sprintf("Model 4 (RMSPE sym LS-SVR): MAPE = %.2f%%\n", mape(y_te, pred4)))
#> Model 1 (MAPE e-SVR): MAPE = 3.59%
#> Model 2 (MAPE sym e-SVR): MAPE = 6.04%
#> Model 3 (RMSPE LS-SVR): MAPE = 3.76%
#> Model 4 (RMSPE sym LS-SVR): MAPE = 5.79%For a full worked example on the Boston Housing dataset — including a 70/30 train–test split, feature standardisation, and comparison against a linear baseline — see vignette("getting-started", package = "psvr").