Systems and methods for training generative machine learning models

A method for unsupervised learning over an input space comprising discrete or continuous variables, and at least a subset of a training dataset of samples of the discrete or continuous variables, to attempt to identify a value of at least one parameter that increases a log-likelihood of the at least a subset of a training dataset with respect to a model, the model expressible as a function of the at least one parameter, the method executed by circuitry including at least one processor and comprising;

• forming a latent space comprising a plurality of random variables, the plurality of random variables comprising one or more discrete random variables and a set of supplementary continuous random variables corresponding to at least a subset of the plurality of random variables;
• forming a first transforming distribution comprising a conditional distribution over the set of supplementary continuous random variables, conditioned on the one or more discrete random variables of the latent space, the first transforming distribution comprising a first smoothing distribution conditional on a first discrete value of the one or more discrete random variables and a second smoothing distribution conditional on a second discrete value of the one or more discrete random variables, the first and second smoothing distributions having the same support;
• forming an encoding distribution comprising an approximating posterior distribution over the latent space, conditioned on the input space;
• forming a prior distribution over the latent space;
• forming a decoding distribution comprising a conditional distribution over the input space conditioned on the set of supplementary continuous random variables;
• and
• training the model based on the first transforming distribution.