Conditional transformation models

By Torsten Hothorn, Thomas Kneib, Peter Buhlmann. 2012

140 citations recorded by the source corpus.

The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models estimate only the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and noise. We propose to relax this common assumption in the framework of transformation models. The novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables. These transformation functions are estimated by regularized optimization of scoring rules for probabilistic forecasts, e.g. the continuous ranked probability score. The corresponding estimated conditional distribution functions are consistent. Conditional transformation models are potentially useful for describing possible heteroscedasticity, comparing spatially varying distributions, identifying extreme events, deriving prediction intervals and selecting variables beyond mean regression effects. An empirical investigation based on a heteroscedastic varying‐coefficient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more beneficial than kernel‐based non‐parametric approaches or parametric generalized additive models for location, scale and shape.

Subfields: Economics and Econometrics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0851b0c5bdffc6d1acd1524d24dfb98de8c4ec32

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Citations in the corpus

Most Likely Transformations (2015, unknown): “, 2012) and conditional transformation models (Hothorn et al., 2014).”
Interpretable Neural Networks for Predicting Mortality Risk using Multi-modal Electronic Health Records (2019, unknown): “However, this work can be extended to cover conditional transformations (e.g., see [31]) or include the multiplication of factors as in traditional general linear models analysis to account for interactions in future work.”
Bernstein flows for flexible posteriors in variational Bayes (2022, unknown): “Transformation models (TMs) have been introduced for fitting potentially complex outcome distributions for probabilistic regression models (Hothorn et al. 2014).”
A general framework for functional regression modelling (2017, methodology): “…boosting as implemented in the R packages mboost (Hothorn et al., 2016) and gamboostLSS (Hofner et al., 2016), exploiting the Kronecker product structure of expansion (3.2) in the case of regular grids and t-constant covariates to increase computational efficiency following Hothorn et al. (2014).”
The functional linear array model (2015, methodology): “Then the out-of-bootstrap (OOB) empirical risk with weights wOOBi = I(wi = 0) is computed and the stopping iteration yielding the lowest empirical risk is chosen (Hothorn et al., 2013).”