Integrating Distributional Copula Regression into the gamboostLSS Package

This project is about extending the gamboostLSS package by flexible copula regression via gradient boosting. Currently the framework only supports univariate responses, but there is a need to model two correlated outcomes with arbitrary marginal distributions (continuous, discrete, binary or mixed) and their dependence structure modelled through the copula. At the core of this project stands the CopulaFamilies() constructor that combines any two existing gamboostLSS family objects with a copula of the user's choice (Gaussian, Clayton, Gumbel or Frank). The constructor automatically detects the marginal types of the input and computes the appropriate joint log-likelihood, as well as the gradients via chain rule. This computation and its results integrate seamlessly into the already existing interface of gamboostLSS(), extending the cvrisk() for multi-dimensional tuning of the stopping hyperparameter and adding a transformation of the dependence parameter to the Kendall's Tau measure for summary() and plot() to establish interpretable dependence estimates. The deliverables for this project include the CopulaFamilies() constructor with automatic full marginal type detection, gradient stabilization for a method of choice (MAD, L2), model selection on the basis of predictive risk minimization, a predict() method for the evaluation of joint cumulative distribution functions and a vignette to demonstrate the full workflow on a real dataset.