The vine pair-copula construction can be used to fit flexible non-Gaussian multivariate distributions to a mix of continuous and discrete variables. With multiple classes, fitting univariate distributions and a vine to each class lead to posterior probabilities over classes that can be used for discriminant analysis. This is more flexible than methods with the Gaussian and/or independence assumptions, such as quadratic discriminant analysis and naive Bayes. Some variable selection methods are studied to accompany the vine copula-based classifier because unimportant variables can make discrimination worse. Simple numerical performance metrics cannot give a full picture of how well a classifier is doing. We introduce categorical prediction intervals and other summary measures to assess the difficulty of discriminating classes. Through extensive experiments on real data, we demonstrate the superior performance of our approaches compared to traditional discriminant analysis methods and random forests when features have different dependent structures for different classes.@en

Regular vines (R-vines) copulas build high dimensional joint densities from arbitrary one-dimensional margins and (conditional) bivariate copula densities. Vine densities enable the computation of all conditional distributions, though the calculations can be numerically intensive. Saturated continuous nonparametric Bayes nets (CNPBN) are regular vines. Computing regression functions from the vine copula density is termed vine regression. The epicycles of regression–including/excluding covariates, interactions, higher order terms, multicollinearity, model fit, transformations, heteroscedasticity, bias–are dispelled. One simply computes the regressions from the vine copula density. Only the question of finding an adequate vine copula remains. Vine regression is applied to a data set from the National Longitudinal Study of Youth relating breastfeeding to IQ. The expected effects of breastfeeding on IQ depend on IQ, on the baseline level of breastfeeding, on the duration of additional breastfeeding and on the values of other covariates. A child given two weeks breastfeeding can expect to increase his/her IQ by 1.5–2 IQ points by adding 10 weeks of breastfeeding, depending on values of other covariates. A child given two years breastfeeding can expect to gain from 0.48–0.65 IQ points from 10 additional weeks. Adding 10 weeks breastfeeding to each of the 3,179 children in this data set has a net present value $50,700,000 according to the Bayes net, compared to $29,000,000 according to the linear regression.

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