Conditional Transformation Models

Abstract

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 only estimate 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 regularised optimisation 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 generalised additive models for location, scale and shape.

References in corpus (1)

• Small area estimation of the homeless in Los Angeles: An application of cost-sensitive stochastic gradient boosting

Cited by in corpus (18)

• A review of predictive uncertainty estimation with machine learning
• Most Likely Transformations
• Probabilistic Forecasting of Sensory Data with Generative Adversarial Networks - ForGAN
• Extending Statistical Boosting - An Overview of Recent Methodological Developments
• A Unified Framework of Constrained Regression
• Regression Diagnostics meets Forecast Evaluation: Conditional Calibration, Reliability Diagrams, and Coefficient of Determination
• Isotonic Distributional Regression
• Top-down Transformation Choice
• Distributional Anchor Regression
• Deep transformation models for functional outcome prediction after acute ischemic stroke
• Truly Multivariate Structured Additive Distributional Regression
• Multivariate Conditional Transformation Models
• Model-based causal feature selection for general response types
• Quantile based modelling of diurnal temperature range with the five-parameter lambda distribution
• Deep Conditional Transformation Models
• Monte Carlo inference for semiparametric Bayesian regression
• If You Like It, GAN It. Probabilistic Multivariate Times Series Forecast With GAN
• Subject-Adaptive Sparse Linear Models for Interpretable Personalized Health Prediction from Multimodal Lifelog Data