Fit a percentage-error SVR / LS-SVR model

Unified entry point for the four model families in the psvr package: MAPE epsilon-SVR (Model 1), symmetric MAPE epsilon-SVR (Model 2), RMSPE LS-SVR (Model 3), and symmetric RMSPE LS-SVR (Model 4). Selection is driven by loss ("mape" or "rmspe") and sym (NULL, +1L, or -1L). The four legacy public fitters (mape_svr(), mape_sym_svr(), rmspe_lssvr(), rmspe_sym_lssvr()) remain available but are slated for deprecation.

Usage

psvr(
  X,
  y,
  loss = c("mape", "rmspe"),
  sym = NULL,
  kernel,
  C = NULL,
  eps = NULL,
  gamma = NULL,
  solver = c("smo", "osqp"),
  tol = 1e-05,
  precondition = "auto",
  alpha_init = NULL,
  alpha_star_init = NULL,
  reg = NULL,
  ...
)

Arguments

X: Numeric matrix of training inputs, one observation per row (N × p).
y: Numeric vector of training targets (length N). Must satisfy y > 0.
loss: One of "mape" (epsilon-SVR with MAPE loss) or "rmspe" (LS-SVR with RMSPE loss).
sym: Symmetry knob. NULL (default) fits the non-symmetric model; +1L enforces even symmetry f(x) = f(-x); -1L enforces odd symmetry f(x) = -f(-x). The symmetric-kernel assumption (Assumption 3 of the paper) must hold; see make_kernel().
kernel: A kernel function created by make_kernel().
C: Regularization parameter C > 0 (loss = "mape" only).
eps: Insensitivity tube half-width eps >= 0 in percentage units (loss = "mape" only).
gamma: Regularization parameter Γ > 0 (loss = "rmspe" only).
solver: Backend for the dual QP, "smo" (default) or "osqp" (loss = "mape" only).
tol: Solver zero-threshold (loss = "mape" only).
precondition: One of "auto" (default), "always", "never", or a positive numeric threshold; controls Remark-17 symmetric rescaling (loss = "rmspe" only). See rmspe_lssvr() for semantics.
alpha_init, alpha_star_init, reg: Reserved for future phases (warm start, extended Lagrangian). Must be NULL in F1.
...: Currently unused; reserved for future extension.

Value

An object of class "psvr_fit", a list with components:

loss: "mape" or "rmspe".
sym: NULL, +1L, or -1L.
kernel: The kernel closure used.
alpha: Dual coefficients. For loss = "mape" this holds α − α* = β; for loss = "rmspe" it holds the LS-SVR α.
b: Bias term.
support_data: Support-vector matrix (after pruning) for loss = "mape", or the full training matrix X for loss = "rmspe".
support_targets: Support-vector targets for loss = "mape"; NULL for loss = "rmspe".
n_train, n_sv, p_train: Training counts.
hyperparameters: Named list (C, eps, gamma, a) with NULL entries for the family that doesn't apply.
solver_meta: Named list (backend, iters, converged, precondition_applied, spectral) describing the solve. The spectral slot is populated only for symmetric MAPE fits (loss = "mape", sym != NULL) and reports Algorithm 2 diagnostics (mu, lambda_min_hat, lambda_max_hat, branch_taken, n_power_iterations); NULL otherwise.

Cross-loss arguments

Some arguments apply only to one family. When loss = "mape", gamma and precondition are ignored (with a warning if supplied non-NULL). When loss = "rmspe", C, eps, solver, and tol are ignored (same warning rule). Default values do not trigger warnings — only user-supplied values do, detected via missing().

Examples

set.seed(1)
X <- matrix(rnorm(40), 20, 2)
y <- rlnorm(20)
K <- make_kernel("rbf", sigma = 1)

fit_mape  <- psvr(X, y, loss = "mape",  kernel = K, C = 10, eps = 5)
fit_rmspe <- psvr(X, y, loss = "rmspe", kernel = K, gamma = 100)
fit_sym   <- psvr(X, y, loss = "rmspe", sym = +1L, kernel = K, gamma = 100)

predict(fit_mape,  X[1:3, , drop = FALSE])
#> [1] 0.8066870 0.7365194 0.8556591
predict(fit_rmspe, X[1:3, , drop = FALSE])
#> [1] 0.9189556 0.7369731 0.8524386
predict(fit_sym,   X[1:3, , drop = FALSE])
#> [1] 1.1583805 0.7439030 0.5084087