Binary outcomes that depend on an ordinal predictor in a nonmonotonic way are common in medical data analysis. Such patterns can be addressed in terms of cutpoints: for example, one looks for two cutpoints that define an interval in the range of the ordinal predictor for which the probability of...

The Gini gain is one of the most common variable selection criteria in machine learning. We derive the exact distribution of the maximally selected Gini gain in the context of binary classification using continuous predictors by means of a combinatorial approach. This distribution provides a...

The R package partykit provides a flexible toolkit for learning, representing, summarizing, and visualizing a wide range of tree-structured regression and classification models. The functionality encompasses: (a) basic infrastructure for representing trees (inferred by any algorithm) so that...

To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this only captures the location of the distribution but over...

Recursive partitioning techniques are established and frequently applied for exploring unknown structures in complex and possibly high-dimensional data sets. The methods can be used to detect interactions and nonlinear structures in a data-driven way by recursively splitting the predictor space...

In the context of binary classification with continuous predictors, we proove two properties concerning the connections between Partial Least Squares (PLS) dimension reduction and between-group PCA, and between linear discriminant analysis and between-group PCA. Such methods are of great...

Classification trees based on imprecise probabilities provide an advancement of classical classification trees. The Gini Index is the default splitting criterion in classical classification trees, while in classification trees based on imprecise probabilities, an extension of the Shannon entropy...

Evidence for variable selection bias in classification tree algorithms based on the Gini Index is reviewed from the literature and embedded into a broader explanatory scheme: Variable selection bias in classification tree algorithms based on the Gini Index can be caused not only by the...

We present a stochastic model for single cell gel electrophoresis (COMET-assay) data. Essential is the use of point process structures, renewal theory and reduction to intensity histograms for further data analysis.