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Select a VCMoE bandwidth by K-fold cross-validation

vcmoe_select_bandwidth.Rd

Selects the kernel bandwidth for a VCMoE model using random K-fold held-out predictive log-likelihood. The selected bandwidth is the candidate with the largest held-out likelihood after ranking fully successful candidates ahead of partial-failure candidates.

Usage

vcmoe_select_bandwidth(
  formula,
  data,
  u,
  k = 2L,
  family = "gaussian",
  bandwidth_grid = NULL,
  folds = 5L,
  u_grid = NULL,
  control = list(),
  label = "align",
  parameterization = "a1_epanechnikov_scaled",
  u_scale = c("unit", "none"),
  seed = NULL,
  refit = TRUE
)

Arguments

formula

A formula of the form y ~ expert_terms | gating_terms.

data

A data frame.

u

Continuous index column name or numeric vector.

k

Number of mixture components. Values from 2 through 10 are supported.

family

Model family. "gaussian", "binomial", and "negative-binomial" are supported.

bandwidth_grid

Candidate bandwidth values. If NULL, uses multiples of the default bandwidth.

folds

Number of random cross-validation folds.

u_grid

Grid where coefficient functions are estimated.

control

Named list passed to vcmoe_fit().

label

Label strategy passed to vcmoe_fit().

u_scale

u scaling strategy passed to vcmoe_fit(). The default selects bandwidths on the unit-scaled analysis domain.

parameterization

Estimator convention passed to vcmoe_fit() for each CV fold and the optional final refit.

seed

Optional random seed for fold assignment and, when control$seed is absent, deterministic CV refits.

refit

Whether to refit the final model on all data using the selected bandwidth.

Value

An object of class vcmoe_bandwidth_selection with fields best_bandwidth, cv_summary, cv_details, cv_folds, fit, and settings.

Details

The default candidate grid is the current Silverman-style default bandwidth multiplied by c(0.5, 0.75, 1, 1.25, 1.5, 2). Fold assignment is made only among complete rows that vcmoe_fit() would keep.

For Gaussian models, validation scoring uses log sum_c pi_c Normal(y | mu_c, sigma_c). For Binomial models, scoring uses log sum_c pi_c Binomial(success | trials, p_c). Binomial Bernoulli and grouped cbind(success, failure) responses are supported. For Negative-Binomial models, scoring uses log sum_c pi_c NB(y | mu_c, theta_c).

Bandwidth selection supports k = 2:10 for Gaussian, Binomial, and Negative-Binomial models. High-k candidates use the same held-out predictive likelihood scoring and should be interpreted together with the returned fit diagnostics. The selected object records the fitting parameterization and u scaling strategy in settings$parameterization and settings$u_scale.