gipsDA

gipsDA provides linear and quadratic discriminant analysis with structured covariance estimation. It uses gips to identify permutation-invariant covariance models, offering regularized estimates for data with symmetric or exchangeable features. Its formula, matrix, and data-frame interfaces follow the conventions of MASS::lda() and MASS::qda().

Models

• gipslda() fits LDA using one projected within-class covariance matrix.
• gipsqda() fits QDA by projecting each class covariance independently.
• gipsmultqda() jointly projects all class covariance matrices, allowing them to share an estimated permutation symmetry.

All three functions support formula, matrix, and data-frame interfaces. Prediction methods provide posterior probabilities and class assignments. LDA additionally provides discriminant coordinates, coefficients, and visualization methods.

Installation

Install the released package from CRAN:

install.packages("gipsDA")

The current source package can also be installed directly from GitHub:

pak::pkg_install("AntoniKingston/gipsDA")

Required dependencies are installed automatically.

Quick start

The example below creates a stratified train/test split of the iris data and fits all three models.

library(gipsDA)

set.seed(42)
train_id <- unlist(
  lapply(split(seq_len(nrow(iris)), iris$Species), sample, size = 35),
  use.names = FALSE
)

train <- iris[train_id, ]
test <- iris[-train_id, ]

lda_fit <- gipslda(Species ~ ., train, optimizer = "BF")
qda_fit <- gipsqda(Species ~ ., train, optimizer = "BF")
joint_qda_fit <- gipsmultqda(Species ~ ., train, optimizer = "BF")

lda_prediction <- predict(lda_fit, test)
qda_prediction <- predict(qda_fit, test)
joint_prediction <- predict(joint_qda_fit, test)

mean(lda_prediction$class == test$Species)
head(lda_prediction$posterior)

The equivalent matrix interface separates predictors from class labels:

x <- as.matrix(iris[, 1:4])
grouping <- iris$Species

fit <- gipslda(x, grouping, optimizer = "BF")
predict(fit, x[1:5, ])$class

Projection options

The principal projection arguments are shared across the models:

• MAP = TRUE uses the maximum a posteriori permutation.
• MAP = FALSE averages projections over retained permutations using their posterior probabilities.
• optimizer = "BF" performs deterministic brute-force optimization and is suitable for smaller problems.
• optimizer = "MH" uses Metropolis-Hastings optimization; use max_iter to control its runtime.

gipslda() also accepts weighted_avg = TRUE, which constructs the pooled scatter estimate from a class-proportion-weighted average of class covariance matrices.

fit <- gipslda(
  Species ~ .,
  iris,
  MAP = FALSE,
  optimizer = "BF",
  weighted_avg = TRUE
)

Prediction rules

LDA supports plug-in, predictive, and debiased prediction:

predict(lda_fit, test, method = "plug-in")
predict(lda_fit, test, method = "predictive")
predict(lda_fit, test, method = "debiased")

Both QDA variants additionally support leave-one-out cross-validation when newdata is omitted:

predict(qda_fit, method = "looCV")
predict(joint_qda_fit, method = "looCV")

LDA diagnostics and visualization

coef(lda_fit)
plot(lda_fit)
pairs(lda_fit, type = "std")
pairs(lda_fit, type = "trellis")

References

Chojecki, A., et al. (2025). Learning Permutation Symmetry of a Gaussian Vector with gips in R. Journal of Statistical Software, 112(7), 1–38. doi:10.18637/jss.v112.i07

The discriminant-analysis implementations are based on the interfaces and algorithms in:

Venables, W. N. and Ripley, B. D. (2002). Modern Applied Statistics with S. Fourth edition. Springer.

License

gipsDA is licensed under GPL (>= 3).