Package {glmdisc}

Type:	Package
Title:	Discretization and Grouping for Logistic Regression
Version:	0.8.1
Date:	2026-10-23
Maintainer:	Adrien Ehrhardt <adrien.ehrhardt@polytechnique.edu>
Description:	A Stochastic-Expectation-Maximization (SEM) algorithm (Celeux et al. (1995) https://inria.hal.science/inria-00074164) associated with a Gibbs sampler which purpose is to learn a constrained representation for logistic regression that is called quantization (Ehrhardt et al. (2019) <doi:10.48550/arXiv.1903.08920>). Continuous features are discretized and categorical features' values are grouped to produce a better logistic regression model. Pairwise interactions between the discretized and grouped features are dynamically added to the model through a Metropolis-Hastings algorithm (Hastings, W. K. (1970) <doi:10.1093/biomet/57.1.97>).
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
Language:	en-US
Config/testthat/edition:	3
Config/Needs/website:	pkgdown
Imports:	gam, graphics, MASS, methods, Rcpp (≥ 1.0.7), RcppNumerical, stats
LinkingTo:	Rcpp, RcppEigen, RcppNumerical
URL:	https://adimajo.github.io/glmdisc/, https://github.com/adimajo/glmdisc
BugReports:	https://github.com/adimajo/glmdisc/issues
Suggests:	covr, DT, knitr, nnet, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
Collate:	'RcppExports.R' 'allClasses.R' 'cut.dataset.R' 'discretize.link.R' 'features.R' 'generic_cutpoints.R' 'generic_discretize.R' 'glmdisc.R' 'initialization.R' 'link_models.R' 'logit_codes.R' 'method_cutpoints.R' 'method_discretize.R' 'method_plot.R' 'method_predict.R' 'methods_disc.R' 'normalizedGini.R' 'semDiscretization.R' 'sem_engine.R' 'utils.R'
Config/roxygen2/version:	8.1.1
NeedsCompilation:	yes
Packaged:	2026-10-23 13:28:46 UTC; adrien
Author:	Adrien Ehrhardt [aut, cre], Vincent Vandewalle [aut], Christophe Biernacki [ctb], Philippe Heinrich [ctb]
Repository:	CRAN
Date/Publication:	2026-11-14 08:20:15 UTC

glmdisc: A package for discretizing continuous features, grouping categorical features' values and optimizing it for logistic regression

Description

The glmdisc package provides two important functions: glmdisc and its associate method discretize.

glmdisc function

The glmdisc function discretizes a training set using an SEM-Gibbs based method.

discretize function

The discretize function will discretize a new input dataset given a discretization scheme of S4 class glmdisc.

cutpoints function

The cutpoints function will provide the cutpoints / groupings of a discretization scheme of S4 class glmdisc in a list.

predict function

The predict function will discretize a raw test set, given a provided discretization scheme of S4 class glmdisc, using the discretize function and return the predicted probabilities.

Miscellaneous

We provide as well the classical show, print, summary functions, as well as normalizedGini that is used to calculate the Gini index (a classical Credit Scoring goodness-of-fit indicator).

Author(s)

Adrien Ehrhardt.

See Also

Useful links:

• https://adimajo.github.io

• Report bugs at https://github.com/adimajo/glmdisc/issues

Obtaining the cutpoints and / or groupings of a discretization

Description

This defines the generic method "cutpoints" which will provide the cutpoints of a discretization scheme of S4 class glmdisc.

This defines the method to provide the cutpoints of a trained glmdisc.

Usage

cutpoints(object)

## S4 method for signature 'glmdisc'
cutpoints(object)

Arguments

Value

A named list with one element per feature. For a numeric feature, a numeric vector with the cutpoints between consecutive levels of the discretization (empty if the feature has a single level). For a factor, a named integer vector that gives, for each level of the factor, the number of the group it was assigned to.

Author(s)

Adrien Ehrhardt.

Examples

# Simulation of a discretized logit model
set.seed(1)
x <- matrix(runif(300), nrow = 100, ncol = 3)
cuts <- seq(0, 1, length.out = 4)
xd <- apply(x, 2, function(col) as.numeric(cut(col, cuts)))
theta <- t(matrix(c(0, 0, 0, 2, 2, 2, -2, -2, -2), ncol = 3, nrow = 3))
log_odd <- rowSums(t(sapply(seq_along(xd[, 1]), function(row_id) {
  sapply(
    seq_along(xd[row_id, ]),
    function(element) theta[xd[row_id, element], element]
  )
})))
y <- rbinom(100, 1, 1 / (1 + exp(-log_odd)))

sem_disc <- glmdisc(x, y,
  iter = 50, m_start = 4, test = FALSE,
  validation = FALSE, criterion = "aic"
)
cutpoints(sem_disc)

Prediction on a raw test set of the best logistic regression model on discretized / grouped data

Description

This function discretizes a user-provided test dataset given a discretization scheme provided by an S4 glmdisc object. It then applies the learnt logistic regression model and outputs its prediction (see predict.glm).

This defines the method "discretize" which will discretize a new input dataset given a discretization scheme of S4 class glmdisc

Usage

discretize(object, data)

## S4 method for signature 'glmdisc'
discretize(object, data)

Arguments

Value

A character matrix with one row per observation of data and one column per feature: the name of the level ("1", "2", ...; "NA" for a missing value) that each value was assigned to.

Author(s)

Adrien Ehrhardt.

Examples

# Simulation of a discretized logit model
set.seed(1)
x <- matrix(runif(300), nrow = 100, ncol = 3)
cuts <- seq(0, 1, length.out = 4)
xd <- apply(x, 2, function(col) as.numeric(cut(col, cuts)))
theta <- t(matrix(c(0, 0, 0, 2, 2, 2, -2, -2, -2), ncol = 3, nrow = 3))
log_odd <- rowSums(t(sapply(seq_along(xd[, 1]), function(row_id) {
  sapply(
    seq_along(xd[row_id, ]),
    function(element) theta[xd[row_id, element], element]
  )
})))
y <- rbinom(100, 1, 1 / (1 + exp(-log_odd)))

sem_disc <- glmdisc(x, y,
  iter = 50, m_start = 4, test = FALSE,
  validation = FALSE, criterion = "aic"
)
discretize(sem_disc, data.frame(x))

Model-based multivariate discretization for logistic regression

Description

This function discretizes a training set using an SEM-Gibbs based method (see References section). It detects numerical features of the dataset and discretizes them ; values of categorical features (of type factor) are regrouped. This is done in a multivariate supervised way. Assessment of the correct model is done via AIC, BIC or test set error (see parameter criterion). Second-order interactions can be searched through the optional interaction parameter using a Metropolis-Hastings algorithm (see References section).

Usage

glmdisc(
  predictors,
  labels,
  interact = TRUE,
  validation = TRUE,
  test = TRUE,
  criterion = "gini",
  iter = 1000,
  m_start = 20,
  reg_type = "poly",
  proportions = c(0.2, 0.2),
  verbose = FALSE,
  fast = FALSE,
  patience = NULL
)

Arguments

Details

This function finds the most appropriate discretization scheme for logistic regression. When provided with a continuous variable X, it tries to convert it to a categorical variable Q which values uniquely correspond to intervals of the continuous variable X. When provided with a categorical variable X, it tries to find the best grouping of its values and subsequently creates categorical variable Q. The goal is to perform supervised learning with logistic regression so that you have to specify a target variable Y denoted by labels. The "discretization" process, i.e. the transformation of X to Q is done so as to achieve the best logistic regression model p(y|e;\theta). It can be interpreted as a special case feature engineering algorithm. When interact = TRUE, the set of pairwise interactions is explored by a Metropolis-Hastings sampler: at each iteration one pair is proposed for addition or removal (with a probability that favors pairs for which a logistic regression on the raw features finds an interaction) and accepted according to the BIC of the logistic regression with and without it. The target of this sampler is the BIC approximation of the posterior of the set of interactions, with a Bernoulli prior given by the pairwise screening, and the proposal is corrected so that it is sampled exactly. The sampler of the thesis (BIC not halved, no proposal correction, unclamped prior) can be restored for comparison with options(glmdisc.mh_scale = 1, glmdisc.mh_hastings = FALSE, glmdisc.mh_clamp = 0). Subsequently, its outputs are: the optimal discretization scheme and the logistic regression model associated with it. We also provide the parameters that were provided to the function and the evolution of the criterion with respect to the algorithm's iterations.

Value

An S4 object of class glmdisc with the following slots:

• parameters: a list with the arguments used to fit the model (test, validation, criterion, iter, m_start, reg_type, interact), the type of each feature (types_data, "numeric" or "factor") and the levels of the factor features;

• best.disc: a list of three elements describing the best discretization scheme found: bestLogisticRegression, the glm fitted on the quantized features (and their interactions, if any); bestLinkFunction, a list with one element per feature that describes how a raw value is assigned to a level (it is used by discretize and predict); and formulaOfBestLogisticRegression, the formula of the logistic regression;

• performance: a list with performance, the normalized Gini index of the best model on the test set (if test = TRUE, otherwise on the validation set if validation = TRUE, otherwise on the training set), and criterionEvolution, the value of the criterion at each iteration;

• disc.data: a data frame with the discretized features (levels named "1", "2", ... and "NA" for missing values) and the labels of the observations on which performance was computed; cont.data: the same observations with the raw features.

Author(s)

Adrien Ehrhardt.

References

Celeux, G., Chauveau, D., Diebolt, J. (1995), On Stochastic Versions of the EM Algorithm. [Research Report] RR-2514, INRIA. 1995. <inria-00074164>

Agresti, A. (2002) Categorical Data. Second edition. Wiley.

See Also

glm, polr

Examples

# Simulation of a discretized logit model
set.seed(1)
x <- matrix(runif(300), nrow = 100, ncol = 3)
cuts <- seq(0, 1, length.out = 4)
xd <- apply(x, 2, function(col) as.numeric(cut(col, cuts)))
theta <- t(matrix(c(0, 0, 0, 2, 2, 2, -2, -2, -2), ncol = 3, nrow = 3))
log_odd <- rowSums(t(sapply(seq_along(xd[, 1]), function(row_id) {
  sapply(
    seq_along(xd[row_id, ]),
    function(element) theta[xd[row_id, element], element]
  )
})))
y <- rbinom(100, 1, 1 / (1 + exp(-log_odd)))

sem_disc <- glmdisc(x, y,
  iter = 50, m_start = 4, test = FALSE,
  validation = FALSE, criterion = "aic"
)
print(sem_disc)

Class glmdisc

Description

Class glmdisc represents a discretization scheme associated with its optimal logistic regression model.

Slots

parameters

The parameters associated with the method.

best.disc

The best discretization scheme found by the method given its parameters.

performance

The performance obtained with the method given its parameters.

disc.data

The discretized data: test set if test is TRUE; if test is FALSE and validation is TRUE, then it provides the discretized validation set. Otherwise, it provides the discretized training set.

disc.data

The continuous data: test set if test is TRUE; if test is FALSE and validation is TRUE, then it provides the discretized validation set. Otherwise, it provides the discretized training set.

Calculating the normalized Gini index

Description

This function calculates the Gini index of a classification rule outputting probabilities. It is a classical metric in the context of Credit Scoring. It is equal to 2 times the AUC (Area Under ROC Curve) minus 1; tied predicted probabilities are given half credit, so the result does not depend on the order of the observations.

Usage

normalizedGini(actual, predicted)

Arguments

Value

A single number between -1 and 1, the normalized Gini index (2 AUC - 1) of predicted for the labels actual: 1 for a perfect ranking, 0 for a ranking no better than chance, negative for an inverted ranking. It is NaN when actual contains a single class.

Author(s)

Adrien Ehrhardt

Examples

normalizedGini(c(1, 1, 1, 0, 0), c(0.7, 0.9, 0.5, 0.6, 0.3))

Plots for the discretized / grouped data

Description

This defines the plot method which will plot some useful graphs for the discretization scheme of S4 class glmdisc

Usage

## S4 method for signature 'glmdisc,missing'
plot(x, y, ...)

Arguments

Value

No return value (NULL, invisibly), called for its side effects: it draws the ROC curve of the model, the risk of each level of every discretized feature, and, for numeric features, a GAM fit of the feature with its discretization. For factor features it also prints the table of the groups of levels.

Examples

# Simulation of a discretized logit model
set.seed(1)
x <- matrix(runif(300), nrow = 100, ncol = 3)
cuts <- seq(0, 1, length.out = 4)
xd <- apply(x, 2, function(col) as.numeric(cut(col, cuts)))
theta <- t(matrix(c(0, 0, 0, 2, 2, 2, -2, -2, -2), ncol = 3, nrow = 3))
log_odd <- rowSums(t(sapply(seq_along(xd[, 1]), function(row_id) {
  sapply(
    seq_along(xd[row_id, ]),
    function(element) theta[xd[row_id, element], element]
  )
})))
y <- rbinom(100, 1, 1 / (1 + exp(-log_odd)))

sem_disc <- glmdisc(x, y,
  iter = 50, m_start = 4, test = FALSE,
  validation = FALSE, criterion = "aic"
)
plot(sem_disc)

Prediction on a raw test set of the best logistic regression model on discretized data

Description

This defines the method "predict" which discretizes a new input dataset given a discretization scheme of S4 class glmdisc and returns the predicted probabilities of class 1.

Usage

predict(object, ...)

## S3 method for class 'glmdisc'
predict(object, predictors, ...)

Arguments

Details

This function discretizes a user-provided test dataset given a discretization scheme provided by an S4 "glmdisc" object. It then applies the learnt logistic regression model and outputs its prediction (see predict.glm).

Value

A numeric vector with the predicted probability of class 1 for each row of predictors.

Examples

# Simulation of a discretized logit model
set.seed(1)
x <- matrix(runif(300), nrow = 100, ncol = 3)
cuts <- seq(0, 1, length.out = 4)
xd <- apply(x, 2, function(col) as.numeric(cut(col, cuts)))
theta <- t(matrix(c(0, 0, 0, 2, 2, 2, -2, -2, -2), ncol = 3, nrow = 3))
log_odd <- rowSums(t(sapply(seq_along(xd[, 1]), function(row_id) {
  sapply(
    seq_along(xd[row_id, ]),
    function(element) theta[xd[row_id, element], element]
  )
})))
y <- rbinom(100, 1, 1 / (1 + exp(-log_odd)))

sem_disc <- glmdisc(x, y,
  iter = 50, m_start = 4, test = FALSE,
  validation = FALSE, criterion = "aic"
)
predict(sem_disc, data.frame(x))

Predicting using a logistic regression fitted with RcppNumerical::fastLR

Description

This function returns a numeric vector containing the probability of each observation of being of class 1 given a vector of logistic regression parameters (usually estimated through RcppNumerical::fastLR).

Usage

predictlogisticRegression(test, parameters)

Arguments

Value

A numeric vector of length nrow(test): the probability of class 1 of each row, 1 / (1 + e^{-x^T \beta}) where x is the row and \beta the parameters.

Examples

# intercept and one covariate: the probabilities are plogis(c(-2, 0, 2))
predictlogisticRegression(cbind(1, c(-2, 0, 2)), c(0, 1))

Print for the glmdisc class

Description

Print for the glmdisc class

Usage

## S3 method for class 'glmdisc'
print(x, ...)

Arguments

Value

The logistic regression fitted on the discretized features (a glm object), invisibly.

Examples

set.seed(1)
x <- matrix(runif(300), nrow = 100, ncol = 3)
y <- rbinom(100, 1, plogis(2 * (x[, 1] > 0.5) - 1))
sem_disc <- glmdisc(x, y,
  iter = 30, m_start = 4, test = FALSE,
  validation = FALSE, criterion = "aic", interact = FALSE
)
print(sem_disc)

Summary for the glmdisc class

Description

Summary for the glmdisc class

Usage

## S3 method for class 'glmdisc'
summary(object, ...)

Arguments

Value

An object of class summary.glm, the summary of the logistic regression fitted on the discretized features.

Examples

set.seed(1)
x <- matrix(runif(300), nrow = 100, ncol = 3)
y <- rbinom(100, 1, plogis(2 * (x[, 1] > 0.5) - 1))
sem_disc <- glmdisc(x, y,
  iter = 30, m_start = 4, test = FALSE,
  validation = FALSE, criterion = "aic", interact = FALSE
)
summary(sem_disc)