## LogisticCopula: A Copula Based Extension of Logistic Regression

An implementation of a method of extending a logistic regression
model beyond linear effects of the co-variates. The extension in is
constructed by first equating the logistic regression model to a naive Bayes
model where all the margins are specified to follow natural exponential
distributions conditional on Y, that is, a model for Y given X that is
specified through the distribution of X given Y, where the columns of X are
assumed to be mutually independent conditional on Y. Subsequently, the
model is expanded by adding vine - copulas to relax the assumption of
mutual independence, where pair-copulas are added in a stage-wise, forward
selection manner. Some heuristics are employed during the process of
selecting edges, as well as the families of pair-copula models. After each
component is added, the parameters are updated by a (smaller) number of
gradient steps to maximise the likelihood. When the algorithm has stopped
adding edges, based the criterion that a new edge should improve the
likelihood more than k times the number new parameters, the parameters are
updated with a larger number of gradient steps, or until convergence.

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