Classical methods for modern applications: synthetic tabular data generation using lightweight discrete response continuous latent variable model

In this paper, we present a lightweight algorithm for modelling tabular data containing both continuous and discrete variables. The method uses empirical marginal distributions and a selected quantile function to transform the data into a continuous latent space, where a distribution of choice, e.g. a multivariate Gaussian, can be efficiently estimated and applied. While this approach is closely related to classical well-established machine learning methods, we present a novel adaptation that fits well within the contemporary computational ecosystem. Unlike in the case of deep architectures, it results in a simple implementation with few dependencies, robust training/estimation, as well as efficient sampling. The transformation preserves complex marginal distributions and correlations, providing high-fidelity models, especially for data with unimodal distributions. One of the key characteristics of the proposed approach is its continuous representation of discrete variables. While highly desirable, this introduces a significant challenge, since a single observation corresponds to a region rather than a point in the latent space. We show that this ambiguity naturally leads to a Monte Carlo expectation-maximisation (MCEM) formulation, whose auxiliary objective can be expressed as a weighted latent-space likelihood. This, in turn, allows conventional maximum-likelihood estimators to be used within an efficient and robust optimisation procedure.