Transformation boosting machines

The broad class of conditional transformation models includes interpretable and simple as well as potentially very complex models for conditional distributions. This makes conditional transformation models attractive for predictive distribution modelling, especially because models featuring interpretable parameters and black-box machines can be understood as extremes in a whole cascade of models. So far, algorithms and corresponding theory was developed for special forms of conditional transformation models only: maximum likelihood inference is available for rather simple models, there exists a tailored boosting algorithm for the estimation of additive conditional transformation models, and a special form of random forests targets the estimation of interaction models. Here, I propose boosting algorithms capable of estimating conditional transformation models of arbitrary complexity, starting from simple shift transformation models featuring linear predictors to essentially unstructured conditional transformation models allowing complex nonlinear interaction functions. A generic form of the likelihood is maximized. Thus, the novel boosting algorithms for conditional transformation models are applicable to all types of univariate response variables, including randomly censored or truncated observations.