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We introduce a new machine-learning-based approach, which we call theIndependent Classifier networks (InClass nets) technique, for thenonparameteric estimation of conditional independence mixture models (CIMMs).We approach the estimation of a CIMM as a multi-class classification problem,since dividing the dataset into different categories naturally leads to theestimation of the mixture model. InClass nets consist of multiple independentclassifier neural networks (NNs), each of which handles one of the variates ofthe CIMM. Fitting the CIMM to the data is performed by simultaneously trainingthe individual NNs using suitable cost functions. The ability of NNs toapproximate arbitrary functions makes our technique nonparametric. Furtherleveraging the power of NNs, we allow the conditionally independent variates ofthe model to be individually high-dimensional, which is the main advantage ofour technique over existing non-machine-learning-based approaches. We derivesome new results on the nonparametric identifiability of bivariate CIMMs, inthe form of a necessary and a (different) sufficient condition for a bivariateCIMM to be identifiable. We provide a public implementation of InClass nets asa Python package called RainDancesVI and validate our InClass nets techniquewith several worked out examples. Our method also has applications inunsupervised and semi-supervised classification problems.

InClass Nets: Independent Classifier Networks for Nonparametric  Estimation of Conditional Independence Mixture Models and Unsupervised  Classification