Semi-Supervised Learning with Mixed Missingness in Finite Mixture Models

Semi-supervised Gaussian finite mixture models for partially labelled data under complete-case, missing completely at random (MCAR), entropy-dependent missing at random (MAR), and mixed MCAR/MAR label-missingness formulations. For the mixed formulation, the source of a missing label may be observed or latent. The package supports equal and component-specific covariance matrices, model fitting, simulation, initialization, prediction, classification performance assessment, and entropy-based diagnostics. A semi-synthetic Blood Transfusion data set is included to illustrate the applied workflow.

SSLfmm

SSLfmm is an R package for semi-supervised Gaussian finite mixture models with partially observed class labels. It supports complete-case, MCAR, entropy-dependent MAR, and mixed MCAR/MAR analyses. In the mixed formulation, the source of a missing label may be known or unknown. The package provides a common workflow for model fitting, simulation, prediction, classification performance assessment, and entropy-based diagnostics.

User-facing API

• fit_sslfmm() — fit cc, mcar, mar, or mixed models.
• initialize_sslfmm() — stable parameter initialization.
• rmix() — simple Gaussian finite-mixture generator.
• simulate_sslfmm() — simulate all four label-observation mechanisms.
• simulate_mixed_missingness() — convenience wrapper for mixed missingness.
• predict() — classes, posterior probabilities, entropy, or all three for an SSLfmm fit.
• classification_performance() — classification metrics and confusion matrix.

Low-level likelihood, parameter-packing, Cholesky, and entropy helpers are internal and intentionally not exported.

Covariance input

Simulation accepts either:

• one shared p x p symmetric positive-definite matrix; or
• one p x p x g array of symmetric positive-definite component covariance matrices.

For p = 1, a length-one scalar is also accepted as a shared variance. Matrix and array inputs are validated explicitly, including dimensions, finite values, symmetry, and positive definiteness.

Fitting supports covariance_type = "equal" and covariance_type = "unequal" throughout initialization, likelihood fitting, and prediction.

Stable simulation return format

simulate_sslfmm() and simulate_mixed_missingness() always return exactly five top-level components:

c("data", "true_setup", "groups", "probs", "raw")

The leading data columns are kept in a stable documented order:

x1, ..., xp, en, missing, label, truth

The current package then adds explicit fields:

observed_missing, latent_missing, missing_source, prob_mar, entropy

en is identical to entropy, and missing is identical to observed_missing. In simulation, latent_missing is the true MCAR-channel trigger.

groups begins with:

mar_group, obs_group, mcar_in_mar, mcar_in_obs

and additionally includes directly useful observed, mcar, mar, and missing row indices.

Mixed missingness indicators

For fit_sslfmm(method = "mixed"):

• indicator = "unknown": the MCAR/MAR source of each missing label is unknown and alpha is estimated jointly.
• indicator = "known": supply the known source of each missing label via missing_source ("mcar" / "mar", or a logical/0-1 MCAR indicator).

An unknown-source fit stores latent_missing_probability, the fitted posterior probability that a missing label came through the MCAR channel.

Minimal example

mu <- matrix(c(-1, 1), nrow = 1, ncol = 2)
sim <- simulate_mixed_missingness(
  n = 200,
  pi = c(0.5, 0.5),
  mu = mu,
  sigma = matrix(1, 1, 1),
  seed = 1
)

x <- as.matrix(sim$data["x1"])
fit <- fit_sslfmm(
  x, sim$data$label,
  g = 2,
  method = "mixed",
  covariance_type = "equal",
  indicator = "unknown",
  n_starts = 5,
  seed = 2
)

predict(fit, x[1:10, , drop = FALSE], type = "posterior")
classification_performance(
  sim$data$truth,
  predict(fit, x),
  predict(fit, x, type = "posterior")
)

Included case-study data

Version 0.2.2 includes the semi-synthetic blood_transfusion data set used in the software-paper application. It can be loaded directly from the package:

library(SSLfmm)

data("blood_transfusion")
head(blood_transfusion)
table(blood_transfusion$missing_indicator)

The complete reference labels are retained for evaluation only; the partially observed response is stored in observed.

Development repository and issue tracker

Development is version controlled in the public GitHub repository:

• https://github.com/wujrtudou/SSLfmm
• Issues: https://github.com/wujrtudou/SSLfmm/issues

The CRAN release remains the recommended installation source for most users.

Installation and checking

Install a built source tarball with:

install.packages("SSLfmm_0.2.2.tar.gz", repos = NULL, type = "source")

Or install an unpacked source directory from a shell with:

R CMD INSTALL SSLfmm

For formal validation:

R CMD build SSLfmm
R CMD check SSLfmm_0.2.2.tar.gz --as-cran