gipsqda: Quadratic Discriminant Analysis with gips covariance...

In gipsDA: Training DA Models Utilizing 'gips'

Quadratic Discriminant Analysis with gips covariance projection

Description

Quadratic discriminant analysis (QDA) using covariance matrices projected via the gips framework to enforce permutation symmetry and improve numerical stability.

Usage

gipsqda(x, ...)

## S3 method for class 'formula'
gipsqda(formula, data, ..., subset, na.action)

## Default S3 method:
gipsqda(x, grouping, prior = proportions,
  nu = 5, MAP = TRUE, optimizer = NULL, max_iter = NULL, ...)

## S3 method for class 'data.frame'
gipsqda(x, ...)

## S3 method for class 'matrix'
gipsqda(x, grouping, ..., subset, na.action)

Arguments

x	(required if no formula is given as the principal argument) a matrix or data frame containing the explanatory variables.
...	Arguments passed to or from other methods.
formula	A formula of the form groups ~ x1 + x2 + .... The response is the grouping factor and the right-hand side specifies the (non-factor) discriminators.
data	An optional data frame, list or environment from which variables specified in formula are preferentially taken.
grouping	(required if no formula is given) a factor specifying the class for each observation.
prior	The prior probabilities of class membership. Must sum to one and have length equal to the number of groups.
nu	Degrees of freedom parameter used internally by covariance projection.
MAP	Logical; if TRUE, maximum a posteriori covariance projection is used.
optimizer	Character string specifying the optimization method used for covariance projection. If NULL, a default choice depending on the problem dimension is used.
max_iter	Maximum number of iterations for stochastic optimizers.
subset	An index vector specifying the cases to be used in the training sample. (NOTE: must be named.)
na.action	A function specifying the action to be taken if NAs are found.

Details

This function is a minor modification of qda, replacing the classical sample covariance estimators by projected covariance matrices obtained using project_covs().

Quadratic discriminant analysis models each class with its own covariance matrix. In gipsqda, these covariance matrices are projected using the gips framework, which enforces permutation symmetry and mitigates singularity and overfitting in high-dimensional or small-sample settings.

Classification can be performed using plug-in, predictive, debiased, or leave-one-out cross-validation rules via predict.gipsqda.

Value

An object of class "gipsqda" containing the following components:

• prior: prior probabilities of the groups

• counts: number of observations in each group

• means: group means

• scaling: group-specific scaling matrices derived from the projected covariance matrices

• ldet: log-determinants of the projected covariance matrices

• lev: class labels

• N: total number of observations

• optimization_info: information returned by the covariance projection optimizer

• call: the matched call

Note

The function may be called with either a formula interface or with a matrix and grouping factor. Arguments subset and na.action, if used, must be named.

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v112.i07")}

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

See Also

qda, predict.gipsqda, gipslda, lda

Examples

tr <- sample(1:50, 25)
train <- rbind(iris3[tr, , 1], iris3[tr, , 2], iris3[tr, , 3])
test <- rbind(iris3[-tr, , 1], iris3[-tr, , 2], iris3[-tr, , 3])
cl <- factor(c(rep("s", 25), rep("c", 25), rep("v", 25)))
z <- gipsqda(train, cl)
predict(z, test)$class

gipsDA documentation built on Feb. 3, 2026, 5:07 p.m.