Generative Trees: Adversarial and Copycat

While Generative Adversarial Networks (GANs) achieve spectacular results on unstructured data like images, there is still a gap on tabular data, data for which state of the art supervised learning still favours to a large extent decision tree (DT)-based models. This paper proposes a new path forward for the generation of tabular data, exploiting decades-old understanding of the supervised task's best components for DT induction, from losses (properness), models (tree-based) to algorithms (boosting). The textitproperness condition on the supervised loss -- which postulates the optimality of Bayes rule -- leads us to a variational GAN-style loss formulation which is textittight when discriminators meet a calibration property trivially satisfied by DTs, and, under common assumptions about the supervised loss, yields "one loss to train against them all" for the generator: the chi2. We then introduce tree-based generative models, textitgenerative trees (GTs), meant to mirror on the generative side the good properties of DTs for classifying tabular data, with a boosting-compliant textitadversarial training algorithm for GTs. We also introduce textitcopycat training, in which the generator copies at run time the underlying tree (graph) of the discriminator DT and completes it for the hardest discriminative task, with boosting compliant convergence. We test our algorithms on tasks including fake/real distinction, training from fake data and missing data imputation. Each one of these tasks displays that GTs can provide comparatively simple -- and interpretable -- contenders to sophisticated state of the art methods for data generation (using neural network models) or missing data imputation (relying on multiple imputation by chained equations with complex tree-based modeling).