Machine Learning for Multi-Output Regression: When should a holistic multivariate approach be preferred over separate univariate ones?

Tree-based ensembles such as the Random Forest are modern classics among statistical learning methods. In particular, they are used for predicting univariate responses. In case of multiple outputs the question arises whether we separately fit univariate models or directly follow a multivariate approach. For the latter, several possibilities exist that are, e.g. based on modified splitting or stopping rules for multi-output regression. In this work we compare these methods in extensive simulations to help in answering the primary question when to use multivariate ensemble techniques.

Deducing neighborhoods of classes from a fitted model

In todays world the request for very complex models for huge data sets is rising steadily. The problem with these models is that by raising the complexity of the models, it gets much harder to interpret them. The growing field of \emph{interpretable machine learning} tries to make up for the lack of interpretability in these complex (or even blackbox-)models by using specific techniques that can help to understand those models better. In this article a new kind of interpretable machine learning method is presented, which can help to understand the partitioning of the feature space into predicted classes in a classification model using quantile shifts. To illustrate in which situations this quantile shift method (QSM) could become beneficial, it is applied to a theoretical medical example and a real data example. Basically, real data points (or specific points of interest) are used and the changes of the prediction after slightly raising or decreasing specific features are observed. By comparing the predictions before and after the manipulations, under certain conditions the observed changes in the predictions can be interpreted as neighborhoods of the classes with regard to the manipulated features. Chordgraphs are used to visualize the observed changes.