VCMoE • VCMoE

VCMoE fits varying-coefficient mixture-of-experts models in R for Gaussian, Binomial, and Negative-Binomial responses.

The package is designed for settings where both the expert response model and the gating probabilities may vary along a continuous coordinate such as time, pseudotime, dose, or space.

Model Overview

VCMoE represents each observation as coming from one of k latent components. For component (c), the expert model describes the response distribution, while the gating model describes the probability of belonging to that component.

For a continuous coordinate u, the gating model has the form:

Pr(C_i = c | X_i, U_i = u) = softmax_c( X_i gamma_c(u) )

The expert mean is modeled by family-specific component functions. For a Gaussian response, the expert model has the form:

E(Y_i | C_i = c, Z_i, U_i = u) = Z_i alpha_c(u)

The current implementation uses Epanechnikov kernel local fitting with a scaled local-linear basis. The public interface supports k = 2:10 with diagnostic outputs for convergence, label alignment, component overlap, and inference quality.

Installation

install.packages("remotes")
remotes::install_github("qc-zhao/VCMoE")

Then load the package:

library(VCMoE)

Quick Gaussian Example

set.seed(1)

sim <- simulate_vcmoe_gaussian(
  n = 300,
  k = 2,
  scenario = "well_separated"
)

fit <- vcmoe_fit(
  y ~ z1 | x1,
  data = sim$data,
  u = sim$data$u,
  k = 2,
  family = "gaussian",
  bandwidth = 0.25
)

coef(fit, "expert")
predict(fit, type = "posterior")
plot_coefficients(fit)

Main Workflows

Task	Function
Fit a VCMoE model	`vcmoe_fit()`
Extract coefficient functions	`coef()`
Predict mean, component means, or posterior probabilities	`predict()`
Select bandwidth by held-out likelihood	`vcmoe_select_bandwidth()`
Bootstrap inference	`vcmoe_bootstrap()`
Analytic-style confidence bands	`vcmoe_confband()`
Generalized likelihood-ratio tests	`vcmoe_glrt()`
Simulate example data	`simulate_vcmoe_gaussian()`, `simulate_vcmoe_binomial()`, `simulate_vcmoe_negbin()`

Tutorials

Start with the Gaussian tutorial:

Gaussian inference tutorial

The tutorial shows how to simulate Gaussian data, fit a VCMoE model, inspect posterior probabilities, plot analytic simultaneous confidence bands, run bootstrap inference, and choose a bandwidth.

Count-model tutorials are separate:

Function Reference

The full function reference is available here:

Reference index

Citation

Please cite:

Zhao Q, Greenwood CMT, Zhang Q. Varying-Coefficient Mixture of Experts Model. arXiv:2601.01699. https://arxiv.org/abs/2601.01699