`R/mdlp.R`

`mdlp_iter.Rd`

This function discretizes a training set using the Minimum Description Length Principle method and the user-provided parameters.

mdlp_iter( predictors, labels, test = FALSE, validation = FALSE, proportions = c(0.3, 0.3), criterion = "gini" )

predictors | The matrix array containing the numeric attributes to discretize. |
---|---|

labels | The actual labels of the provided predictors (0/1). |

test | Boolean : True if the algorithm should use predictors to construct a test set on which to search for the best discretization scheme using the provided criterion (default: TRUE). |

validation | Boolean : True if the algorithm should use predictors to construct a validation set on which to calculate the provided criterion using the best discretization scheme (chosen thanks to the provided criterion on either the test set (if true) or the training set (otherwise)) (default: TRUE). |

proportions | The list of the (2) proportions wanted for test and validation set. Only the first is used when there is only one of either test or validation that is set to TRUE. Produces an error when the sum is greater to one. Useless if both test and validation are set to FALSE. Default: list(0.2,0.2). |

criterion | The criterion ('gini','aic','bic') to use to choose the best discretization scheme among the generated ones (default: 'gini'). Nota Bene: it is best to use 'gini' only when test is set to TRUE and 'aic' or 'bic' when it is not. When using 'aic' or 'bic' with a test set, the likelihood is returned as there is no need to penalize for generalization purposes. |

This function discretizes a dataset containing continuous features \(X\) in a supervised way, i.e. knowing observations of a binomial random variable \(Y\) which we would like to predict based on the discretization of \(X\).
To do so, the `MDLP`

alorithm dichotomizes \(X\) and puts the subsequent two values in the ‘‘discretized'' categorical feature \(E\). It chooses the cut-off point so as to minimize the resulting entropy and goes on in the subsequent two sub-spaces it just created.
In the context of Credit Scoring, a logistic regression is fitted between the ‘‘discretized'' features \(E\) and the response feature \(Y\). As a consequence, the output of this function is the discretized features \(E\), the logistic regression model of \(E\) on \(Y\) and the parameters used to get this fit.

Enea, M. (2015), speedglm: Fitting Linear and Generalized Linear Models to Large Data Sets, https://CRAN.R-project.org/package=speedglm

HyunJi Kim (2012). discretization: Data preprocessing, discretization for classification. R package version 1.0-1. https://CRAN.R-project.org/package=discretization

Fayyad, U. M. and Irani, K. B.(1993). Multi-interval discretization of continuous-valued attributes for classification learning, *Artificial intelligence*, **13**, 1022–1027.

`glm`

, `speedglm`

, `discretization`

Adrien Ehrhardt

# Simulation of a discretized logit model 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 <- stats::rbinom(100, 1, 1 / (1 + exp(-log_odd))) mdlp_iter(x, y)#>#> #> #>#>#> #> #>#>#> #> #>#> Generalized Linear Model of class 'speedglm': #> #> Call: speedglm::speedglm(formula = stats::formula("labels ~ ."), data = Filter(function(x) (length(unique(x)) > 1), cbind(data.frame(sapply(disc$Disc.data, as.factor), stringsAsFactors = TRUE), data_train[, sapply(data_train, is.factor), drop = FALSE])), family = stats::binomial(link = "logit"), weights = NULL, fitted = TRUE) #> #> Coefficients: #> (Intercept) X22 #> 0.74 -1.80 #>